A281189 a(n) is the first composite number having the same base-(2n) digits as its prime factors (with multiplicity), excluding zero digits (or 0 if no such composite number exists).

15, 85, 57, 85, 1111, 185, 4119, 4369, 489, 451, 13315, 679, 26533, 985, 1057, 1285, 179503, 1387, 82311, 2005, 2649, 2047, 4663957, 2509, 2761, 3385, 3097, 3277, 243895, 4207, 16246817, 4369, 4577, 471651, 5401, 5629, 607839, 466429, 483731, 6817, 1009273, 10587, 1132547, 8119, 8401, 798731, 990583, 9809, 1411791, 1062517

Offset: 1

Author

Ely Golden and Robert G. Wilson v, Jan 16 2017

Keywords

• base
• nonn

Comments

Bisection of A278981.

Conjecture: a(n) always exceeds 0.

If a(n) = 0 then it must be the case that there exists no more than one prime of the form (2n)^m + 1. Otherwise, the product of two such primes would satisfy the condition of A278981 in base 2n.

Records: 15, 85, 1111, 4119, 4369, 13315, 26533, 179503, 4663957, 16246817, 75927167, 120872069, 335192766, ..., .

a(76) > 2^27.

Examples

			a(2) = A278981(4) since 85 is the least composite number which satisfies the criterion of A278981.
		

Links

• Ely Golden and Robert G. Wilson v, Table of n, a(n) for n = 1..75

Crossrefs

Cf. A278981, A280270.

Programs

Mathematica

g[n_] := g[n] = Flatten[ Table[#[[1]], {#[[2]]}] & /@ FactorInteger@ n]; f = Compile[{{b, _Integer}}, Block[{c = b^2}, While[ PrimeQ@ c || DeleteCases[ Sort[ IntegerDigits[c, b]], 0] != DeleteCases[ Sort[ Flatten[ IntegerDigits[ g[c], b]]], 0], c++]; c]]; Table[ f[b], {b, 2, 80, 2}]

Formula

a(n) = A278981(2n).