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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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified June 15 03:12 EDT 2024. Contains 373402 sequences. (Running on oeis4.)