

A272713


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


1



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
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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+=qp; p=nextprime(p+1))) \\ Charles R Greathouse IV, May 05 2016


CROSSREFS

Cf. A025475, A034707, A067377, A050936.
Sequence in context: A304771 A316514 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



