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A256351 Composites in base 10 that remain composite in exactly seven bases b, 2 <= b <= 10, expansions interpreted as decimal numbers.

%I A256351 #21 Apr 09 2024 15:59:57
%S A256351 8,9,15,16,21,22,25,28,34,75,87,91,93,94,106,111,123,141,143,145,147,
%T A256351 155,172,201,205,214,217,237,255,298,304,305,363,371,376,377,385,388,
%U A256351 395,403,411,423,428,442,458,466,471,473,483,495,501,505,507,531,533
%N A256351 Composites in base 10 that remain composite in exactly seven bases b, 2 <= b <= 10, expansions interpreted as decimal numbers.
%H A256351 Sebastian Petzelberger, <a href="/A256351/b256351.txt">Table of n, a(n) for n = 1..10000</a>
%H A256351 Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_024.htm">PP&P Puzzle 24: Primes in several bases</a>
%p A256351 f:= proc(b,x) local L,i;
%p A256351 L:= convert(x,base,b);
%p A256351 isprime(add(10^(i-1)*L[i],i=1..nops(L)))
%p A256351 end proc:
%p A256351 select(t -> not isprime(t) and nops(select(f,[$2..9],t))=2, [$1..1000]); # _Robert Israel_, Mar 26 2015
%t A256351 fQ[n_] := CompositeQ@ n && Count[ CompositeQ[ FromDigits[ IntegerDigits[n, #]] & /@ Range[2, 9]], True] == 6; Select[ Range@ 500, fQ] (* _Robert G. Wilson v_, Mar 26 2015 *)
%Y A256351 Cf. A052026, A256350 - A256356.
%Y A256351 Cf. A038537, A052027, A052028, A052029, A052030, A052031, A052032, A084482.
%Y A256351 Cf. A052033, A236356.
%K A256351 nonn,base
%O A256351 1,1
%A A256351 _Sebastian Petzelberger_, Mar 25 2015