A256114 Numbers n such that digit_product(n^2) = (digit_product(n))^2 and n mod 10 > 0.
1, 2, 3, 101, 102, 103, 104, 105, 201, 202, 203, 205, 301, 302, 303, 305, 401, 402, 403, 405, 501, 502, 503, 504, 505, 506, 507, 508, 509, 601, 602, 603, 605, 609, 661, 701, 702, 703, 705, 708, 709, 801, 802, 803, 805, 901, 902, 903, 905, 906, 983
Offset: 1
Examples
digit_product(661^2) = digit_product(436921) = 1296 = 36^2 = (digit_product(661))^2.
Links
- Reiner Moewald, Table of n, a(n) for n = 1..15212
Programs
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Magma
[t: j in [1..9], k in [0..100] | &*Intseq(t^2) eq &*Intseq(t)^2 where t is 10*k+j]; // Bruno Berselli, Jun 23 2015
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Maple
pdigs:= n -> convert(convert(n,base,10),`*`): select(t -> pdigs(t^2)=pdigs(t)^2, [seq(seq(10*k+j,j=1..9),k=0..1000)]); # Robert Israel, Jun 05 2015
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Mathematica
pod[n_] := Times@@ IntegerDigits@ n; Select[ Range[10^4], Mod[#, 10] > 0 && pod[#]^2 == pod[#^2] &] (* Giovanni Resta, Jun 23 2015 *)
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Python
def product_digits(n): results = 1 while n > 0: remainder = n % 10 results *= remainder n = (n-remainder)/10 return results pos = 0 for a in range(1,1000000): if product_digits(a*a) == (product_digits(a))*(product_digits(a)) and (a%10 > 0): pos += 1 print(pos, a)
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