A123994 Smallest number k such that prime(n)^k is a sum of 3 consecutive primes.

64, 57, 2, 2, 107, 203, 1133, 1, 2, 1

Offset

2,1

Comments

a(13) through a(23): { 1, 2, 3, 8, 1, 4, 6, 1, 729, 5, 1 }.

a(12) > 5387. a(24) > 3320.

Smallest prime p such that p^n is equal to the sum of 3 consecutive primes is given by A122706(n).

Links

Table of n, a(n) for n=2..11.

Example

a(1) does not exist because there is no power of 2 that is a sum of 3 consecutive primes.
prime(5)^2 = 11^2 = 121 can be written as 37+41+43, therefore a(5)=2.

Prog

(PARI) { A123994(n) = my(k, t1, t2, t3, m); k=0; while(1, k++; m=prime(n)^k; t1=precprime(m/3); t2=nextprime(m/3); t3=m-t1-t2; if( ispseudoprime(t3) && ( (t3<t1 && t3==precprime(t1-1)) || (t3>t2 && t3==nextprime(t2+1)) ), return(k)); ); }

Crossrefs

Cf. A122706.

Sequence in context: A252486 A188828 A331224 * A248770 A272297 A291094

Adjacent sequences: A123991 A123992 A123993 * A123995 A123996 A123997

Keyword

hard,more,nonn

Author

Alexander Adamchuk, Oct 31 2006, Nov 02 2006

Extensions

Corrected by R. J. Mathar, Jan 13 2007

a(8)-a(11) from Max Alekseyev, Apr 24 2010

Status

approved