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A136975
Numbers k such that k and k^2 use only the digits 1, 2, 3, 5 and 7.
1
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
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
Sequence in context: A034905 A031153 A136976 * A136973 A276037 A221743
KEYWORD
base,nonn
AUTHOR
Jonathan Wellons (wellons(AT)gmail.com), Jan 22 2008
STATUS
approved