A235914 Odd primes p = 2*m + 1 with m*(m-1) - prime(m) and m*(m+1) - prime(m) both prime.

13, 17, 23, 29, 31, 43, 73, 89, 181, 229, 313, 367, 379, 557, 631, 683, 1021, 1069, 1093, 1151, 1303, 1459, 1471, 1663, 1733, 1831, 1871, 2411, 2473, 2791, 2843, 2887, 3673, 3691, 3793, 3797, 3863, 4001, 4139, 4261, 5261, 5431, 6091, 6301, 6661, 6737, 6883, 7489, 7523, 7873

Offset

1,1

Comments

By the conjecture in A235912, this sequence should have infinitely many terms.

Links

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

Example

a(1) = 13 since none of 1*2 - prime(1) = 0, 1*2 - prime(2) = -1, 2*3 - prime(3) = 1 and 2*4 + 1 = 9 = 4*5 - prime(5) is prime, but 2*6 + 1 = 13, 5*6 - prime(6) = 30 - 13 = 17 and 6*7 - prime(6) = 42 - 13 = 29 are all prime.

Mathematica

PQ[n_]:=n>0&&PrimeQ[n]
q[n_]:=PQ[n(n-1)-Prime[n]]&&PQ[n(n+1)-Prime[n]]
n=0; Do[If[q[(Prime[k]-1)/2], n=n+1; Print[n, " ", Prime[k]]], {k, 2, 1000}]

Crossrefs

Cf. A000040, A235727, A235912.

Sequence in context: A179924 A274321 A316603 * A050716 A217046 A141076

Adjacent sequences: A235911 A235912 A235913 * A235915 A235916 A235917

Keyword

nonn

Author

Zhi-Wei Sun, Jan 16 2014

Status

approved