A136975 Numbers k such that k and k^2 use only the digits 1, 2, 3, 5 and 7.

1, 5, 11, 15, 35, 111, 115, 235, 335, 715, 1235, 2715, 3335, 3511, 3515, 3711, 12335, 27115, 33335, 33515, 35711, 37115, 72335, 75711, 111235, 123335, 132335, 177515, 333335, 333515, 357115, 572115, 575515, 577515, 723335, 757115, 1233335, 1312335, 1323335, 3333335, 3333515, 3512511, 5227115, 5772115, 7233335, 11212115, 11277115, 11735515

Offset: 1

Author

Jonathan Wellons (wellons(AT)gmail.com), Jan 22 2008

Keywords

• base
• nonn

Comments

Generated with DrScheme.

Sequence is infinite; e.g., it contains 3...35 = (10^n-1)/3 + 2 for all n. - Robert Israel, Nov 24 2015

a(n) mod 100 can be only 11, 15 or 35 for n > 2. So if a(n) is a prime number, a(n) mod 100 = 11 for n > 2. Initial prime values of a(n) are 11, 3511 and 12375511 for n > 2. - Altug Alkan, Nov 25 2015

Examples

			757313127132715^2 = 573523172527531752317223271225.
		

Links

• Jonathan Wellons, Table of n, a(n) for n = 1..330
• J. Wellons, Tables of Shared Digits [archived]

Crossrefs

Cf. A001742, A034905.

Programs

Maple

f2:= proc(n) local L; convert(convert(n^2,base,10),set) intersect {4,6,8,9,0} = {} end proc:
S:= {0}: A:= {}:
for d from 1 to 8 do
  S:={seq(seq(10*s+j,j=[1,2,3,5,7]),s=S)};
  A:= select(f2,S) union A;
od:
sort(convert(A,list)); # Robert Israel, Nov 24 2015, corrected Sep 03 2020

Mathematica

w = {1, 2, 3, 5, 7}; Select[Range[1, 10^7, 2], Union[IntegerDigits@ #, IntegerDigits[#^2], w] == w &] (* Michael De Vlieger, Nov 25 2015 *)