27374 is a numbers whose arithmetic and multiplicative digital roots are not digits of the number itself but whose arithmetic root is equal to the number of digits in the number. Here the arithmetic digital root is 5 and the multiplicative digital root is 8. The number of digits in the number (5) corresponds to the arithmetic digital root.

The sequence can be generated as follows (permalink):

INPUT

L=[]

for n in [1..40000]:

  b=10

  if sum(n.digits(b))%(b-1)!=0:

    dr=sum(n.digits())%(b-1)

  else:

    dr=9

  number=n

  while len(number.digits())>1:

    number=prod(number.digits())

  if dr not in n.digits() and (number not in n.digits() and dr==len(n.digits())):

    L.append(n)

print(L)

print(len(L))

OUTPUT (from 27374 to 40000 shown)

[ ... 27374, 27383, 27392, 27419, 27437, 27473, 27491, 27617, 27626, 27662, 27671, 27689, 27698, 27716, 27734, 27743, 27761, 27779, 27788, 27797, 27833, 27869, 27878, 27887, 27896, 27914, 27923, 27932, 27941, 27968, 27977, 27986, 28112, 28121, 28148, 28166, 28184, 28211, 28229, 28238, 28283, 28292, 28328, 28337, 28346, 28364, 28373, 28382, 28418, 28436, 28463, 28481, 28499, 28616, 28634, 28643, 28661, 28679, 28688, 28697, 28733, 28769, 28778, 28787, 28796, 28814, 28823, 28832, 28841, 28868, 28877, 28886, 28922, 28949, 28967, 28976, 28994, 29111, 29129, 29147, 29174, 29192, 29219, 29228, 29237, 29246, 29264, 29273, 29282, 29291, 29327, 29372, 29399, 29417, 29426, 29444, 29462, 29471, 29489, 29498, 29624, 29642, 29669, 29678, 29687, 29696, 29714, 29723, 29732, 29741, 29768, 29777, 29786, 29822, 29849, 29867, 29876, 29894, 29912, 29921, 29939, 29948, 29966, 29984, 29993, 31127, 31136, 31163, 31172, 31199, 31217, 31226, 31244, 31262, 31271, 31316, 31334, 31343, 31361, 31379, 31388, 31397, 31424, 31433, 31442, 31469, 31478, 31487, 31496, 31613, 31622, 31631, 31649, 31667, 31676, 31694, 31712, 31721, 31739, 31748, 31766, 31784, 31793, 31838, 31847, 31874, 31883, 31919, 31937, 31946, 31964, 31973, 31991, 32117, 32126, 32144, 32162, 32171, 32216, 32234, 32243, 32261, 32279, 32288, 32297, 32324, 32342, 32378, 32387, 32414, 32423, 32432, 32441, 32468, 32477, 32486, 32612, 32621, 32648, 32666, 32684, 32711, 32729, 32738, 32747, 32774, 32783, 32792, 32828, 32837, 32846, 32864, 32873, 32882, 32927, 32972, 32999, 33116, 33134, 33143, 33161, 33179, 33188, 33197, 33224, 33242, 33278, 33287, 33314, 33341, 33368, 33377, 33386, 33413, 33422, 33431, 33449, 33467, 33476, 33494, 33611, 33638, 33647, 33674, 33683, 33719, 33728, 33737, 33746, 33764, 33773, 33782, 33791, 33818, 33827, 33836, 33863, 33872, 33881, 33899, 33917, 33944, 33971, 33989, 33998, 34124, 34133, 34142, 34169, 34178, 34187, 34196, 34214, 34223, 34232, 34241, 34268, 34277, 34286, 34313, 34322, 34331, 34349, 34367, 34376, 34394, 34412, 34421, 34439, 34448, 34466, 34484, 34493, 34619, 34628, 34637, 34646, 34664, 34673, 34682, 34691, 34718, 34727, 34736, 34763, 34772, 34781, 34799, 34817, 34826, 34844, 34862, 34871, 34889, 34898, 34916, 34934, 34943, 34961, 34979, 34988, 34997, 36113, 36122, 36131, 36149, 36167, 36176, 36194, 36212, 36221, 36248, 36266, 36284, 36311, 36338, 36347, 36374, 36383, 36419, 36428, 36437, 36446, 36464, 36473, 36482, 36491, 36617, 36626, 36644, 36662, 36671, 36689, 36698, 36716, 36734, 36743, 36761, 36779, 36788, 36797, 36824, 36833, 36842, 36869, 36878, 36887, 36896, 36914, 36941, 36968, 36977, 36986, 37112, 37121, 37139, 37148, 37166, 37184, 37193, 37211, 37229, 37238, 37247, 37274, 37283, 37292, 37319, 37328, 37337, 37346, 37364, 37373, 37382, 37391, 37418, 37427, 37436, 37463, 37472, 37481, 37499, 37616, 37634, 37643, 37661, 37679, 37688, 37697, 37724, 37733, 37742, 37769, 37778, 37787, 37796, 37814, 37823, 37832, 37841, 37868, 37877, 37886, 37913, 37922, 37931, 37949, 37967, 37976, 37994, 38138, 38147, 38174, 38183, 38228, 38237, 38246, 38264, 38273, 38282, 38318, 38327, 38336, 38363, 38372, 38381, 38399, 38417, 38426, 38444, 38462, 38471, 38489, 38498, 38624, 38633, 38642, 38669, 38678, 38687, 38696, 38714, 38723, 38732, 38741, 38768, 38777, 38786, 38813, 38822, 38831, 38849, 38867, 38876, 38894, 38939, 38948, 38966, 38984, 38993, 39119, 39137, 39146, 39164, 39173, 39191, 39227, 39272, 39299, 39317, 39344, 39371, 39389, 39398, 39416, 39434, 39443, 39461, 39479, 39488, 39497, 39614, 39641, 39668, 39677, 39686, 39713, 39722, 39731, 39749, 39767, 39776, 39794, 39839, 39848, 39866, 39884, 39893, 39911, 39929, 39938, 39947, 39974, 39983, 39992]

27374 stabilises after about 67 generations to a single block and a single glider.

27374 can be expressed as a "digit equation" in at least two ways viz. 2×7−3=7+4 and 2×7−(3+7)=4.