A063844 Smith numbers which are also base-2 pseudoprimes.

645, 4369, 13747, 15709, 88357, 157641, 642001, 656601, 1507963, 2269093, 2313697, 4101637, 7428421, 7429117, 8388607, 22669501, 26296401, 27218269, 27336673, 28011001, 32701297, 34487601, 36507801, 37167361, 47903701, 54215161, 71804161, 72498253, 74411131, 82279741, 86438857, 86530621, 93614521, 96135601, 97863529

Offset: 1

Author

Shyam Sunder Gupta, Aug 25 2001

Keywords

• base
• nonn

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A001567 and A006753.

Programs

Mathematica

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, If[!PrimeQ@ k && PowerMod[2, k-1, k] == 1, AppendTo[lst, k]]; k++]; Select[ lst, fQ]