The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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