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

1,1

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.

Links

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

Formula

a(n) = A278981(2n).

Example

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

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}]

Crossrefs

Cf. A278981, A280270.

Sequence in context: A050405 A241220 A279740 * A206383 A020136 A176033

Adjacent sequences: A281186 A281187 A281188 * A281190 A281191 A281192

Keyword

base,nonn

Author

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

Status

approved