A235661 Primes p with p*(p+1) - prime(p) prime.

2, 3, 5, 11, 19, 29, 37, 41, 53, 61, 71, 89, 131, 137, 149, 157, 233, 263, 271, 281, 293, 331, 337, 359, 389, 431, 433, 439, 457, 487, 499, 571, 617, 631, 659, 701, 739, 751, 761, 809, 859, 877, 907, 911, 1009, 1019, 1031, 1033, 1087, 1093

Offset

1,1

Comments

This sequence is a subsequence of A235592.

By the conjecture in A232353, this sequence should have infinitely many terms.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Example

2 is a term because 2*3 - prime(2) = 3 is prime.
3 is a term because 3*4 - prime(3) = 7 is prime.
5 is a term because 5*6 - prime(5) = 19 is prime.

Mathematica

PQ[n_]:=PrimeQ[n(n+1)-Prime[n]]
n=0; Do[If[PQ[Prime[k]], n=n+1; Print[n, " ", Prime[k]]], {k, 1, 1000}]

Crossrefs

Cf. A000040, A232353, A234695, A235592, A235613, A235614.

Sequence in context: A231479 A084758 A087582 * A070865 A084697 A037082

Adjacent sequences: A235658 A235659 A235660 * A235662 A235663 A235664

Keyword

nonn

Author

Zhi-Wei Sun, Jan 13 2014

Status

approved