cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A110996 Powers equal to (sum of first k primes) plus 1, for some k >= 0.

Original entry on oeis.org

1, 441, 970225, 1464100, 194379364, 1303400915339554201
Offset: 1

Views

Author

Walter Kehowski, Sep 30 2005

Keywords

Comments

I have checked for powers out to the 250000th prime and the last element found is at the 6420th prime, 64067. It is interesting to note that the only powers so far are squares. Finding a higher power would be interesting.

Examples

			1 is a term (corresponding to k=0), since it is the empty sum plus 1. - _N. J. A. Sloane_, Dec 02 2015
441 is a term since sum(primes<=59) = 440 and 441 = 21^2.

Crossrefs

Cf. A007504, A110979, A110997, A264858.
Intersection of A001597 and A014284.

Programs

  • Maple
    with(numtheory); egcd := proc(n) local L; L:=map(proc(z) z[2] end, ifactors(n)[2]); igcd(op(L)) end: s := proc(n) option remember; local p; if n=1 then [1,2] else [n,s(n-1)[2]+ithprime(n)] fi end; t := proc(n) option remember; [n,s(n)[2]+1] fi end; PW:=[]; for z to 1 do for j from 1 to 250000 do if egcd(t(j)[2])>1 then PW:=[op(PW),t(j)] fi od od; PW;
  • PARI
    lista(nn) = { print1(1, ", "); s = 1; for(k=1, nn, s += prime(k); if(ispower(s) || s==1, print1(s, ", ")););} \\ Altug Alkan, Nov 29 2015

Extensions

New term 1 prepended by Altug Alkan, Nov 29 2015
a(6) from Jinyuan Wang, Aug 09 2023

A110997 Powers equal to (sum of first k primes) minus 1.

Original entry on oeis.org

1, 4, 9, 16, 27, 128, 196, 839056, 7796654478001
Offset: 1

Views

Author

Walter Kehowski, Sep 30 2005

Keywords

Comments

I have checked out to the first 250000 primes but the last entry is at the 504th prime, 3607.

Examples

			128 is a term because 128 = -1 + Sum_{i=1..10} prime(i) = 2^7.

Crossrefs

Cf. A007504, A110979, A110996.
Intersection of A001597 and A237589.

Programs

  • Maple
    with(numtheory); egcd := proc(n) local L; L:=map(proc(z) z[2] end, ifactors(n)[2]); igcd(op(L)) end: s := proc(n) option remember; local p; if n=1 then [1,2] else p:=ithprime(n); [n,s(n-1)[2]+p] fi end; t := proc(n) option remember; [n,s(n)[2]-1] end; PW:=[]; for z to 1 do for j from 1 to 250000 do if egcd(t(j)[2])>1 or t(j)[2]=1 then PW:=[op(PW),t(j)] fi od od; PW;
  • Mathematica
    s = 0; Do[s = s + Prime[n]; If[s == 2 || GCD @@ Transpose[ FactorInteger[s - 1]][[2]] > 1, Print[s - 1]], {n, 10^6}] (* Robert G. Wilson v, Oct 02 2005 *)

Extensions

Initial 1 and a(9) added by Jinyuan Wang, Aug 10 2023
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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