A112786 Starting from P0=3, the sequence list the minimum prime P1>P0 for which the expression P=P1+P0+1 is also a prime. The search then restarts from P1.

3, 7, 11, 17, 19, 23, 29, 31, 41, 47, 53, 59, 67, 71, 79, 83, 89, 101, 109, 113, 127, 149, 157, 173, 179, 193, 227, 229, 233, 257, 263, 277, 293, 307, 311, 331, 359, 367, 383, 389, 397, 431, 449, 457, 461, 467, 479, 487, 503, 509, 521, 541, 587, 593, 599, 601

Offset

0,1

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Example

3+5+1=9 is not a prime.
3+7+1=11 is a prime: 7 is in the sequence.
7+11+1=19 is a prime: 11 is in the sequence.
11+13+1=25 is not a prime.
11+17+1=29 is a prime: 17 is in the sequence.

Maple

P:=proc(n) local i, w; w:=3; for i from 3 by 1 to n do if isprime(w+ithprime(i)+1) then print(ithprime(i)); w:=ithprime(i); fi; od; end: P(500);

Mathematica

f[n_]:=Module[{p=NextPrime[n]}, While[!PrimeQ[n+p+1], p=NextPrime[p]]; p]; Join[{p=3}, Table[p=f[p], {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Feb 07 2012 *)
nxt[p_]:=Module[{np=NextPrime[p]}, While[!PrimeQ[p+np+1], np=NextPrime[np]]; np]; NestList[nxt, 3, 60] (* Harvey P. Dale, Jun 05 2023 *)

Crossrefs

Cf. A000040

Sequence in context: A118000 A121640 A319258 * A023211 A038981 A065376

Adjacent sequences: A112783 A112784 A112785 * A112787 A112788 A112789

Keyword

easy,nonn

Author

Amarnath Murthy, Jan 02 2006

Extensions

More terms from Paolo P. Lava and Giorgio Balzarotti, Mar 07 2007

Edited by N. J. A. Sloane at the suggestion of Stefan Steinerberger, Jun 07 2007

Status

approved