A206553 Least prime p > 3 such that 2^n + p*2^floor((n+1)/2) - 1 is prime.

5, 5, 13, 7, 5, 5, 7, 7, 11, 13, 13, 11, 5, 11, 37, 11, 5, 23, 13, 47, 89, 13, 19, 19, 11, 7, 19, 23, 17, 13, 19, 43, 29, 79, 61, 17, 191, 43, 337, 53, 29, 17, 13, 13, 29, 11, 19, 11, 11, 13, 43, 163, 29, 13, 7, 53, 23, 97, 31, 29, 41, 83, 79, 23, 191, 97

Offset

1,1

Links

Pierre CAMI, Table of n, a(n) for n = 1..10000

Example

2^1+5*2^1-1 = 11 prime so a(1) = 5.
2^2+5*2^1-1 = 13 prime so a(2) = 5.

Prog

PFGW64 from Primeform group and SRYPTIFY
command : pfgw64 -f in.txt
in.txt file :
SCRIPT
DIM kk
DIM nn, 0
DIM mm
DIMS tt
OPENFILEOUT myfil, prem.txt
LABEL loopn
SET nn, nn+1
IF nn>10000 THEN END
IF nn%2==0 THEN SET mm, nn/2
IF nn%2==1 THEN SET mm, nn/2+1
SET kk, 2
LABEL loopk
SET kk, kk+1
SETS tt, %d, %d, %d, %d\ ; nn; kk; p(kk); mm
PRP (2^(nn-mm)+p(kk))*2^mm-1, tt
IF ISPRP THEN GOTO a
IF ISPRIME THEN GOTO a
GOTO loopk
LABEL a
WRITE myfil, tt
GOTO loopn
(Haskell)
a206553 n = head [p | p <- drop 2 a000040_list,
                      a010051 (2^n + p*2^(div (n+1) 2) - 1) == 1]
-- Reinhard Zumkeller, Feb 10 2012

Crossrefs

Cf. A206554.

Cf. A010051, A000040.

Sequence in context: A302676 A370297 A339947 * A122213 A224067 A049735

Adjacent sequences: A206550 A206551 A206552 * A206554 A206555 A206556

Keyword

nonn

Author

Pierre CAMI, Feb 09 2012

Status

approved