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

1,2

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

Links

Jonathan Wellons, Table of n, a(n) for n = 1..330

J. Wellons, Tables of Shared Digits [archived]

Example

757313127132715^2 = 573523172527531752317223271225.

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 *)

Crossrefs

Cf. A001742, A034905.

Sequence in context: A034905 A031153 A136976 * A136973 A276037 A221743

Adjacent sequences: A136972 A136973 A136974 * A136976 A136977 A136978

Keyword

base,nonn,changed

Author

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

Status

approved