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A235914 Odd primes p = 2*m + 1 with m*(m-1) - prime(m) and m*(m+1) - prime(m) both prime. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 2 23:30 EST 2021. Contains 349445 sequences. (Running on oeis4.)