A059322 First differences of sequence of consecutive safe primes.

2, 4, 12, 24, 12, 24, 24, 60, 12, 48, 36, 84, 12, 24, 84, 12, 24, 60, 24, 132, 120, 24, 24, 96, 36, 168, 96, 24, 12, 48, 72, 48, 36, 96, 204, 84, 120, 12, 24, 36, 108, 240, 12, 120, 240, 60, 24, 60, 36, 24, 96, 48, 36, 264, 156, 156, 24, 60, 84, 60, 72, 48, 12, 120, 24

Offset

1,1

Comments

Except for (5,7) and (7,11), all terms are divisible by 12, since safe primes are congruent to 5 modulo 6 except 7 and safe_prime + 6 is not a safe prime. Closest safe primes differ by 12 like (11,23) or (83207,83219).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..5001 from G. C. Greubel)

Formula

a(n) = A005385(n+1) - A005385(n). [corrected by Harvey P. Dale, Jan 12 2011 and Zak Seidov, Sep 19 2016]

Mathematica

Differences[Select[Prime[Range[500]], PrimeQ[(#-1)/2]&]]  (* Harvey P. Dale, Jan 12 2011 *)

Prog

(PARI) list(lim) = {my(p1 = 5); forprime(p2 = 7, lim, if(isprime((p2-1)/2), print1(p2-p1, ", "); p1 = p2)); } \\ Amiram Eldar, Mar 02 2025

Crossrefs

Cf. A005385, A033299.

Sequence in context: A295954 A364753 A052416 * A163908 A332666 A230481

Adjacent sequences: A059319 A059320 A059321 * A059323 A059324 A059325

Keyword

nonn,changed

Author

Labos Elemer, Jan 26 2001

Extensions

Offset corrected by Amiram Eldar, Mar 02 2025

Status

approved