A363422 Numbers k which satisfy k = concat(a,b,...) and a*b*... = reverse(k), for some two or more a,b,...
351, 621, 886, 5931, 86673, 97533, 425322, 430762, 920781, 3524751, 4495491, 4834872, 5594151, 5941971, 6218001, 6801381, 6916671, 8630841, 32331001, 44235301, 57982563, 67968432, 68577483, 69617484, 71673981, 88873491, 89943354, 119910901, 338752611
Offset: 1
Examples
153 = 3*51. 1395 = 5*9*31. 1945944 = 44*9*54*91. 1008126 = 6*21*8001. 171548496 = 6*94*84*51*71.
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Programs
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Python
# Find numbers with a de-concatenation that multiplies to their reverse. import math def digits(x): y = [] while x>0: y = [x%10] + y x//=10 return y def check(x): xx = digits(x) if xx[0] < xx[-1]: return for i in range(1,2**(len(xx)-1)): for dnum,digit in enumerate(xx): if dnum==0: thisProd = [xx[0]] elif i&(2**(dnum-1)): if digit==0: break thisProd += [digit] else: thisProd[-1] = thisProd[-1]*10+digit answer = math.prod(thisProd) if not answer%10==xx[0]: continue if digits(answer)[-1::-1]==xx: print('\r'+str(thisProd).replace(', ','x')[1:-1]) return return i=0 while True: i += 1 if not i%10000: print('\r'+str(i),end='') check(i)
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