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%I #10 Nov 11 2019 04:33:02
%S 645,4369,13747,15709,88357,157641,642001,656601,1507963,2269093,
%T 2313697,4101637,7428421,7429117,8388607,22669501,26296401,27218269,
%U 27336673,28011001,32701297,34487601,36507801,37167361,47903701,54215161,71804161,72498253,74411131,82279741,86438857,86530621,93614521,96135601,97863529
%N Smith numbers which are also base-2 pseudoprimes.
%H Amiram Eldar, <a href="/A063844/b063844.txt">Table of n, a(n) for n = 1..10000</a>
%e 645 is a member since 645=3*5*43, sum of digits of 645 is 6+4+5=15, sum of digits of prime factors = 3+5+4+3=15 and 2^644 (mod 645) == 1.
%t fQ[n_] := Block[{id = Sort@ IntegerDigits@ n, fid = Sort@ Flatten[ IntegerDigits@ Table[#[[1]], {#[[2]]}] & /@ FactorInteger@ n]}, While[ id[[1]] == 0, id = Drop[id, 1]]; While[ fid[[1]] == 0, fid = Drop[fid, 1]]; id != fid && Plus @@ id == Plus @@ fid]; k = 1; lst = {}; While[k < 10^8, !PrimeQ@ k && PowerMod[2, k-1, k] == 1, AppendTo[lst, k]]; k++]; Select[ lst, fQ]
%Y Intersection of A001567 and A006753.
%K base,nonn
%O 1,1
%A _Shyam Sunder Gupta_, Aug 25 2001
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