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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). 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 18 20:32 EST 2018. Contains 299330 sequences. (Running on oeis4.)