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

1,1

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, ...

Links

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

Example

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.

Prog

(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

Crossrefs

Cf. A025475, A034707, A067377, A050936.

Sequence in context: A316514 A352179 A304468 * A316285 A018200 A306049

Adjacent sequences: A272710 A272711 A272712 * A272714 A272715 A272716

Keyword

nonn

Author

Altug Alkan, May 05 2016

Extensions

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

Status

approved