A089895 Prime numbers p for which there exists an integer q > p such that the sum of all primes <= p equals the sum of all primes between p+1 and q.

3, 3833, 468872968241

Offset

1,1

Comments

Primes p such that 2*A034387(p) is a term of A034387. - Max Alekseyev, Aug 24 2023

No other terms below 10^13. - Max Alekseyev, Aug 25 2023

Links

Table of n, a(n) for n=1..3.

Carlos Rivera, Puzzle 18.- Some special sums of consecutive primes, The Prime Puzzles & Problems Connection. See specifically the large solution by Giovanni Resta.

Example

2+3+5+...+3833 = 3847+...+5557 and therefore 3833 is in the sequence.

Mathematica

a[m_] := Module[{pLst, cumsum, p, q, k, target, idx}, pLst = Prime[Range[PrimePi[m]]]; cumsum = Accumulate[pLst]; pairs = {}; For[k = 1, k <= Length[pLst], k++, p = pLst[[k]]; target = 2*cumsum[[k]]; idx = FirstPosition[Drop[cumsum, k], target]; If[idx =!= Missing["NotFound"], q = pLst[[k + First[idx]]]; If[q > p, AppendTo[pairs, p]; ]]]; pairs]; a[10000] (* Robert P. P. McKone, Aug 25 2023 *)

Prog

(PARI) p=2; s=2; q=3; t=3; while(p<512345678900, while(s<=t, p=nextprime(p+1); s=s+p; t=t-p); if (s==t, print1(p, ", "), ); while(t<s, q=nextprime(q+1); t=t+q); if(s==t, print1(p, ", "), ))

Crossrefs

Sequence in context: A200735 A226984 A196628 * A116213 A136544 A024048

Adjacent sequences: A089892 A089893 A089894 * A089896 A089897 A089898

Keyword

more,nonn,bref

Author

Randy L. Ekl, Jan 10 2004

Extensions

Better definition from Adam M. Kalman (mocha(AT)clarityconnect.com), Jun 16 2005

Edited by Max Alekseyev, Aug 24 2023

Status

approved