




OFFSET

1,1


COMMENTS

The 6th term is too large to include in the data section (see Example section or the bfile).
Primes of the form sum_{j=1..u} j^x for some x>0, u>1. (Since the case of x=1 leads to the triangular numbers with no additional primes, this is equivalent to the definition.)
Primes in A000330 (x=2), or in A000537 (x=3), or in A000538 (x=4), or in A000539 (x=5) etc. See A164312 for the corresponding x values.


LINKS

N. J. A. Sloane, Table of n, a(n) for n = 1..6


EXAMPLE

a(1) = 1^1 + 2^1 = 3.
a(2) = 1^2 + 2^2 = 5.
a(3) = 1^4 + 2^4 = 17.
a(4) = 1^8 + 2^8 = 257.
a(5) = 1^16 + 2^16 = 65537.
a(6) = 1^1440 + 2^1440 + 3^1440 + 4^1440 + 5^1440 = 3.287049497374559048967261852*10^1006 = 3287049497374559048967261852 ... 458593539025033893379.


MATHEMATICA

lst={}; Do[s=0; Do[If[PrimeQ[s+=n^x], AppendTo[lst, s]; Print[Date[], s]], {n, 4!}], {x, 7!}]; lst


CROSSREFS

Cf. A000215, A070592, A019434, A092506, A093179, A100270, A123599.
Sequence in context: A273871 A078726 A019434 * A125045 A093179 A067387
Adjacent sequences: A164304 A164305 A164306 * A164308 A164309 A164310


KEYWORD

nonn


AUTHOR

Vladimir Joseph Stephan Orlovsky, Aug 12 2009


EXTENSIONS

Edited by R. J. Mathar, Aug 22 2009
Corrected by N. J. A. Sloane, Nov 23 2015 at the suggestion of Jaroslav Krizek.


STATUS

approved



