A272713 Prime powers (p^k, k>=2) that are the sum of consecutive prime numbers.

8, 49, 121, 128, 169, 243, 625, 841, 961, 1331, 1369, 1681, 1849, 2209, 3125, 5329, 6241, 6859, 6889, 8192, 10201, 11449, 11881, 12167, 12769, 16384, 18769, 22801, 24649, 26569, 32768, 36481, 39601, 44521

Offset: 1

Author

Altug Alkan, May 05 2016

Keywords

• nonn

Comments

In other words, prime powers (p^k, k>=2) that are the sum of two or more consecutive prime numbers.

Intersection of A025475 and A034707.

Terms of this sequence are 2^3, 7^2, 11^2, 2^7, 13^2, 3^5, 5^4, 29^2, ...

Examples

			8 is a term because 8 = 2^3 = 3 + 5.
49 is a term because 49 = 7^2 = 13 + 17 + 19.
121 is a term because 121 = 11^2 = 37 + 41 + 43.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..4469

Crossrefs

Cf. A025475, A034707, A067377, A050936.

Programs

PARI

list(lim)=my(v=List(),n=1,p,q,t,s); while(1, t=primes(n++); p=2; q=t[n]; s=vecsum(t); if(s>lim, return(Set(v))); while(s<=lim, if(isprimepower(s)>1, listput(v,s)); q=nextprime(q+1); s+=q-p; p=nextprime(p+1))) \\ Charles R Greathouse IV, May 05 2016

Extensions

a(9)-a(34) from Charles R Greathouse IV, May 05 2016