OFFSET
1,1
COMMENTS
Subsequence of A067380.
LINKS
Jon E. Schoenfield, Table of n, a(n) for n = 1..3000
EXAMPLE
a(1) = 34421 = Sum_{i=57..127} prime(i) = Sum_{i=226..248} prime(i) = Sum_{i=527..535} prime(i) = Sum_{i=654..660} prime(i) = Sum_{i=1382..1384} prime(i) and
a(3) = 235493 = Sum_{i=50..284} prime(i) = Sum_{i=120..300} prime(i) = Sum_{i=123..301} prime(i) = Sum_{i=334..424} prime(i) = Sum_{i=7701..7703} prime(i)
are expressible in 5 ways as the sum of two or more consecutive primes.
MATHEMATICA
m=3*7!; lst={}; Do[p=Prime[a]; Do[p+=Prime[b]; If[PrimeQ[p]&&p<Prime[m]*3+8, AppendTo[lst, p]], {b, a+1, m, 1}], {a, m}]; lst1=Sort[lst]; lst={};
Do[If[lst1[[n]]==lst1[[n+1]]&&lst1[[n]]==lst1[[n+2]]&&lst1[[n]]==lst1[[n+3]]&&lst1[[n]]==lst1[[n+4]], AppendTo[lst, lst1[[n]]]], {n, Length[lst1]-4}]; Union[lst]
PROG
(Magma) M:=1695000; P:=PrimesUpTo(M); S:=[0]; for p in P do t:=S[#S]+p; if #S ge 3 then if t-S[#S-2] gt M then break; end if; end if; S[#S+1]:=t; end for; c:=[0:j in [1..M]]; for C in [2..#S-1] do if IsEven(C) then L:=1; else L:=#S-C; end if; for j in [1..L] do s:=S[j+C]-S[j]; if s gt M then break; end if; if IsPrime(s) then c[s]+:=1; end if; end for; end for; [j:j in [1..M]|c[j] ge 5]; // Jon E. Schoenfield, Dec 25 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Joseph Stephan Orlovsky, Aug 15 2009
EXTENSIONS
Examples added by R. J. Mathar, Aug 19 2009
a(10)-a(28) from Donovan Johnson, Sep 16 2009
a(29)-a(31) from Jon E. Schoenfield, Dec 25 2021
STATUS
approved