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%I #26 Nov 12 2019 12:50:43
%S 88,104,113,114,116,117,118,119,120,125,126,131,133,134,136,140,141,
%T 142,144,145,146,147,148,150,155,156,157,159,160,161,162,163,164,165,
%U 166,170,171,172,175,177,178,179,180,181,182,185,186,187,188,189,190,191,192
%N Numbers k such that 2^k contains each decimal digit at least twice.
%C A subsequence of A130694.
%C Motivated by J. Merickel's question about the least power of 2 in which all digits 0-9 occur a prime number of times. The first 4 terms of this sequence are all such that this is the case for all but one digit; see Examples.
%C Beyond 184, the numbers 195-197 and 229 are the only exponents < 10^4 which are not in this sequence. Is 229 the largest such number?
%H J. Merickel, <a href="http://groups.yahoo.com/group/primenumbers/message/24399">Are these new questions?</a>, Yahoo! group "primenumbers", Aug 24 2012.
%H James Merickel, <a href="/A215830/a215830.txt">Are these new questions?</a>, message 24399 in primenumbers Yahoo group, Aug 24, 2012.
%e Digit counts for 2^n:
%e .
%e n\d| 0 1 2 3 4 5 6 7 8 9
%e ---+-----------------------------
%e 88| 5 2 2 2 3 3 2 2 4* 2
%e 104| 5 3 6* 2 3 2 5 2 2 2
%e 113| 5 3 3 2 3 5 4* 3 2 5
%e 114| 3 7 2 5 4* 2 2 2 5 3
%e .
%e *nonprime counts
%o (PARI) is_A215830(n)={my(c=vector(10),N=[1<<n,0]);while(N=divrem(N[1],10),c[N[2]+1]++);vecmin(c)>1}
%K nonn,base
%O 1,1
%A _M. F. Hasler_, Aug 25 2012