A263654 - OEIS

A263654

Values of k such that 3^k is a concatenation of two primes.

3, 5, 6, 9, 10, 15, 17, 19, 28, 35, 42, 47, 51, 55, 56, 58, 63, 73, 80, 83, 85, 87, 94, 100, 112, 127, 129, 132, 198, 202, 268, 282, 287, 299, 316, 325, 345, 362, 400, 412, 447, 459, 519, 525, 549, 620, 631, 727, 756, 854, 856, 892, 1031, 1038, 1140, 1175, 1241

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

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..57.

EXAMPLE

3^3 = 27 = concat(2,7);

3^5 = 243 = concat(2,43);

3^6 = 729 = concat(7,29);

3^9 = 19683 = concat(19,683).

MAPLE

with(numtheory): P:= proc(q) local a, k, n, ok; a:=0;

for n from 1 to q do ok:=0;

for k from 1 to ilog10(3^n) do if isprime(trunc(3^n/10^k)) and isprime(3^n mod 10^k) then ok:=1;

break; fi; od; if ok=1 then a:=a+1; lprint(a, n); fi; od; end: P(10^10);

MATHEMATICA

ctpQ[k_]:=AnyTrue[Boole[PrimeQ[Table[FromDigits/@TakeDrop[IntegerDigits[3^k], n], {n, IntegerLength[ 3^k-1]}]]], #=={1, 1}&]; Select[Range[1250], ctpQ] (* Harvey P. Dale, Apr 17 2024 *)

CROSSREFS

Cf. A255898.

Sequence in context: A094598 A367334 A329003 * A122194 A225005 A053091

Adjacent sequences: A263651 A263652 A263653 * A263655 A263656 A263657

KEYWORD

nonn,base

AUTHOR

Paolo P. Lava, Oct 23 2015

STATUS

approved