A072669 Primes of the form prime(x) + prime(x+1) - 1.

7, 11, 17, 23, 29, 41, 59, 67, 83, 89, 127, 137, 151, 197, 239, 257, 307, 359, 383, 389, 409, 433, 449, 461, 479, 491, 547, 557, 563, 599, 617, 647, 683, 701, 739, 751, 761, 797, 809, 827, 839, 863, 881, 929, 977, 1063, 1087, 1103, 1163, 1229, 1249, 1283, 1289, 1319, 1373

Offset: 1

Author

Herman H. Rosenfeld (herm3(AT)pacbell.net), Aug 12 2002

Keywords

• nonn
• easy

Comments

Consider m such that prime(m) + prime(m+1) = prime(k) + 1 for some k; sequence gives prime(k).

A118072 is a subsequence, hence this sequence is infinite on Dickson's conjecture. - Charles R Greathouse IV, Apr 18 2013

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001043, A092738, A072666, A072667.

Programs

Mathematica

f[n_] := Prime[n] + Prime[n + 1] - 1; f[ # ] & /@ Select[ Range[120], PrimeQ[ f[ # ]] &] (* Robert G. Wilson v, Apr 14 2004 *)
Select[Total[#]-1&/@Partition[Prime[Range[200]],2,1],PrimeQ] (* Harvey P. Dale, Aug 06 2012 *)

PARI

p=2;forprime(q=3,1e6,if(isprime(p+q-1),print1(p+q-1", "));p=q) \\ Charles R Greathouse IV, Apr 18 2013

Extensions

Definition reworded by Jorge Coveiro, Apr 12 2004

Edited by N. J. A. Sloane, Sep 14 2008 at the suggestion of R. J. Mathar