

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




OFFSET

1,1


COMMENTS



LINKS



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=tp); if (s==t, print1(p, ", "), ); while(t<s, q=nextprime(q+1); t=t+q); if(s==t, print1(p, ", "), ))


CROSSREFS



KEYWORD

more,nonn,bref


AUTHOR



EXTENSIONS

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


STATUS

approved



