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

Author

Reiner Moewald, Mar 15 2015

Keywords

• nonn
• base

Comments

Contains i*10^d + j for i>=1, j mod 10 > 0, j < 10^d/(20*i+1). - Robert Israel, Jun 05 2015

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

Crossrefs

Cf. A007954, A256115.

Programs

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

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

Mathematica

pod[n_] := Times@@ IntegerDigits@ n; Select[ Range[10^4], Mod[#, 10] > 0 && pod[#]^2 == pod[#^2] &] (* Giovanni Resta, Jun 23 2015 *)

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)