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A235806 Odd primes p with (p^2 - 1)/4 - prime((p - 1)/2) and (p^2 - 1)/4 - prime((p + 1)/2) both prime. 3
7, 11, 19, 29, 41, 43, 53, 59, 89, 109, 139, 179, 181, 229, 379, 401, 421, 431, 541, 587, 659, 811, 991, 1069, 1103, 1117, 1231, 1259, 1459, 1471, 1619, 1709, 1831, 1951, 2179, 2791, 2797, 2833, 2851, 3001, 3391, 3571, 3617, 3631, 3637, 3671, 3793, 3863, 3929, 3967 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

By the conjecture in A235805, this sequence should have infinitely many terms.

LINKS

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

EXAMPLE

a(1) = 7 since neither (3^2-1)/4 - prime((3-1)/2) = 0 nor (5^2-1)/4 - prime((5+1)/2) = 1 is prime, but (7^2-1)/4 - prime((7-1)/2) = 12 - 5 = 7 and (7^2-1)/4 - prime((7+1)/2) = 12 - 7 = 5 are both prime.

MATHEMATICA

q[n_]:=PrimeQ[n(n+1)-Prime[n]]&&PrimeQ[n(n+1)-Prime[n+1]]

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

CROSSREFS

Cf. A000040, A235592, A235727, A235805.

Sequence in context: A192187 A053403 A032672 * A238501 A133425 A103802

Adjacent sequences:  A235803 A235804 A235805 * A235807 A235808 A235809

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, Jan 16 2014

STATUS

approved

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Last modified January 21 04:53 EST 2020. Contains 331104 sequences. (Running on oeis4.)