A130973 Number of primes between successive pairs of twin primes, for a(n) > 0.

1, 1, 2, 1, 4, 3, 4, 2, 1, 3, 1, 2, 3, 10, 4, 7, 4, 3, 2, 1, 2, 18, 2, 2, 17, 1, 2, 6, 9, 3, 1, 1, 1, 8, 3, 2, 15, 1, 4, 1, 1, 7, 7, 4, 4, 3, 4, 1, 1, 7, 2, 5, 1, 5, 18, 2, 5, 4, 3, 1, 5, 1, 18, 12, 2, 8, 1, 4, 2, 5, 4, 1, 1, 1, 9, 10

Offset

1,3

Comments

a(k) corresponds to the k-th term in the isolated prime sequence A007510 or A134797. a(1) corresponds to 23. a(2) corresponds to 37. a(3) corresponds to 47 and 53. - Enrique Navarrete, Jan 28 2017

Lengths of the runs of consecutive integers in A176656. - R. J. Mathar, Feb 19 2017

Links

Ruud H.G. van Tol, Table of n, a(n) for n = 1..10000

Chris K. Caldwell, The PrimePages.

Omar E. Pol, Determinación geométrica de los números primos y perfectos.

Mathematica

Select[Differences[Select[Range[1000], AnyTrue[Prime[#] + {2, -2}, PrimeQ] &]] - 1, Positive] (* Paolo Xausa, Jan 18 2026 *)

Prog

(PARI) lista(nn)= my(v=vector(nn), p=3, q, i=1, j=0, k=1, n=0); while(isprime(p-2) || isprime(p+2), p=nextprime(p+1)); q=nextprime(p+1); forprime(r=q+2, oo, i++; if(q-p>2 && r-q>2, if(i==(j+1), k++, v[n++]=k; n<nn||break; k=1); j=i); p=q; q=r); v; \\ Ruud H.G. van Tol, Jan 08 2026

Crossrefs

Cf. A001223, A007510 (isolated primes), A027883, A048614, A048198, A052011, A052012, A061273, A076777, A073784, A082602, A088700, A176656, A179067 (clusters of twin primes).

Sequence in context: A105239 A261366 A283166 * A093779 A231898 A276638

Adjacent sequences: A130970 A130971 A130972 * A130974 A130975 A130976

Keyword

easy,nonn

Author

Omar E. Pol, Aug 23 2007

Status

approved