A165287 Primes which are the sum of at least 3 consecutive odd nonprimes (A014076) >1.

61, 73, 97, 107, 163, 179, 197, 233, 239, 257, 263, 271, 307, 331, 349, 359, 367, 397, 409, 419, 421, 461, 467, 479, 487, 503, 523, 547, 571, 593, 599, 613, 617, 631, 659, 677, 691, 709, 727, 733, 743, 757, 761, 787, 809, 811, 821, 827, 839, 857, 859, 881, 883, 907, 929, 967, 997, 1019, 1039

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

15+21+25 = 61, 9+15+21+25+27 = 97.

Maple

N:= 1000: # for terms <= N
tmax:= 2*ceil(N/6)+7:
T:= remove(isprime, [seq(i, i=3..tmax, 2)]):
S:= ListTools:-PartialSums([0, op(T)]):
R:= {}:
for m from 3 by 2 while S[m] <= N do
  for j from 1 do
    v:= S[m+j]-S[j];
    if v > N then break fi;
    if isprime(v) then R:= R union {v} fi
od od:
sort(convert(R, list)); # Robert Israel, Apr 17 2026

Mathematica

lst={}; Do[If[PrimeQ[m], Continue[]]; s=m; Do[If[PrimeQ[n], Continue[]]; s+=n; If[PrimeQ[s], If[s<=2917, AppendTo[lst, s]]], {n, m+2, 2*6!, 2}], {m, 1, 2*6!, 2}]; lst=Take[Union@lst, 200]

Prog

(PARI) N=1000; v=vector(N); L=listcreate(); n=9; while(n<N, if(!isprime(n), listput(L, n)); n=n+2); vv=Vec(L); forstep(k=3, #vv, 2, for(offs=1, #vv-k+1, s=sum(i=offs, offs+k-1, vv[i]); if(isprime(s)&&s<=N, v[s]=1))); for(n=60, #v, if(v[n], print1(n, ", "))) \\ Ralf Stephan, Nov 26 2013

Crossrefs

Cf. A014076, A106091.

Sequence in context: A180555 A039478 A109549 * A139944 A179012 A227980

Adjacent sequences: A165284 A165285 A165286 * A165288 A165289 A165290

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Sep 13 2009

Extensions

Edited by Ralf Stephan, Nov 26 2013

Corrected by Robert Israel, Apr 17 2026

Status

approved