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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.
1
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
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
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