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

Author

Alexander Adamchuk, Oct 31 2006, Nov 02 2006

Keywords

• hard
• more
• nonn

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).

Examples

			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.
		

Crossrefs

Cf. A122706.

Programs

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) && ( (t3t2 && t3==nextprime(t2+1)) ), return(k)); ); }

Extensions

Corrected by R. J. Mathar, Jan 13 2007

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