A179289 Smallest index k such that prime(k)*2^n-1 is prime, or zero if there is no prime.

1, 1, 2, 1, 4, 1, 2, 3, 4, 3, 2, 1, 11, 3, 22, 1, 4, 1, 18, 7, 4, 23, 6, 23, 18, 5, 44, 23, 4, 1, 14, 3, 11, 2, 11, 7, 11, 2, 18, 28, 8, 16, 2, 102, 4, 9, 11, 3, 8, 5, 174, 24, 63, 3, 2, 103, 22, 23, 130, 1, 22, 16, 18, 2, 19, 55, 14, 41, 34, 15

Offset

1,3

Comments

Define partial sum S(N)=Sum(n=1...N) of n , T(N)=Sum(n=1...N) of k(n) The ratio T(N)/S(N) --> approx 0.5236 as N --> infinity.

It is conjectured that a(42228) is the first 0 term. This corresponds to the first Riesel number, 509203, which happens to be prime. See A101036. - T. D. Noe, Mar 23 2011

Links

Table of n, a(n) for n=1..70.

Formula

a(n) = 1 for n = A000043(k) - 1, the Mersenne exponents minus 1. - T. D. Noe, Mar 23 2011

Mathematica

sik[n_]:=Module[{c=2^n, k=1}, While[!PrimeQ[Prime[k]*c-1], k++]; k]; Array[ sik, 70] (* The program will NOT identify cases where no prime satisfies the definition.  See the second comment. *) (* Harvey P. Dale, Jan 10 2016 *)

Prog

(Other) SCRIPT / DIM nn, 0 / DIM kk / DIMS st / LABEL loopn / SET nn, nn+1 / IF nn>10000 THEN END / SET kk, 0 / LABEL loopk / SET kk, kk+1 / SET st, %d, %d, %d\,; nn; kk; p(kk) / PRP p(kk)*2^nn-1 / IF ISPRIME THEN GOTO loopn / GOTO loopk / / This file is the in.txt file / The command is PFGW -f in.txt / The results are in the file pfgw-prime.log for small n / and in the pfgw.log file for greatest n / Program PFGW from Primeform Group /
(PARI) a(n) = {my(k=1); while (!isprime(prime(k)*2^n-1), k++); k; } \\ Michel Marcus, Sep 16 2019

Crossrefs

Cf. A126715.

Sequence in context: A105584 A072064 A105498 * A083414 A334890 A171174

Adjacent sequences: A179286 A179287 A179288 * A179290 A179291 A179292

Keyword

nonn

Author

Pierre CAMI, Jul 09 2010

Status

approved