A139021 a(0)=2. a(n) = smallest prime > a(n-1) such that (Sum_{k=0..n} a(k)) is a power of a prime.

2, 3, 11, 13, 227, 307, 461, 463, 2609, 2683, 58757, 58831, 137777, 138007, 17179469033, 17179470433, 240518567327, 240518567479, 19807040628566083882989513161, 19807040628566083882989513433, 324478939577169594614874645075239, 324478939577169594614874645093097

Offset

0,1

Links

Max Alekseyev, Table of n, a(n) for n = 0..31 (shortened by N. J. A. Sloane, Jan 13 2019)

Example

The corresponding prime powers are 2 + 3 = 5^1, 2 + 3 + 11 = 2^4, 2 + 3 + 11 + 13 = 29^1, etc.

Maple

a := [2, 3] ; while true do as := add(i, i=a) ; p := nextprime(op(-1, a)) ; while nops(numtheory[factorset](p+as)) > 1 do p := nextprime(p) ; od; a := [op(a), p] ; print(a) ; od: # R. J. Mathar, Apr 28 2008

Prog

(PARI) { printA139021() = my(a=2, s=2); print1(2, ", "); for(n=2, 100, if( s%2==0, until(isprimepower(s+a), a=nextprime(a+1)), t=log(s+a)\log(2) + 1; while( !ispseudoprime(2^t-s), t++); a=2^t-s; ); s+=a; print1(a, ", "); ); } /* Max Alekseyev, Oct 17 2015 */

Crossrefs

Cf. A139019, A139022.

Sequence in context: A139052 A076491 A105226 * A176038 A293827 A145771

Adjacent sequences: A139018 A139019 A139020 * A139022 A139023 A139024

Keyword

nonn

Author

Leroy Quet, Apr 06 2008

Extensions

9 more terms from R. J. Mathar, Apr 28 2008

a(14)-a(19) from Donovan Johnson, Nov 26 2008

a(20)-a(21) from Max Alekseyev, Oct 14 2012

a(22)-a(31) in b-file from Max Alekseyev, Oct 17 2015

Status

approved