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A235727 Odd primes p with (p^2 - 1)/4 - prime((p - 1)/2) and (p^2 - 1)/4 + prime((p - 1)/2) both prime. 5
7, 11, 19, 23, 41, 73, 83, 109, 197, 211, 229, 271, 379, 461, 541, 631, 641, 659, 859, 991, 1031, 1049, 1051, 1093, 1103, 1217, 1429, 1451, 1879, 2063, 2131, 2287, 2341, 2411, 3019, 3257, 3461, 3659, 3673, 3691, 3709, 3917, 3967, 4409, 4463, 4519, 5279, 5303, 5471, 5477 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

By the conjecture in A235728, 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) = 1 nor (5^2-1)/4 + prime((5-1)/2) = 9 is prime, but (7^2-1)/4 - prime((7-1)/2) = 12 - 5 = 7 and (7^2-1)/4 + prime((7-1)/2) = 12 + 5 = 17 are both prime.

MATHEMATICA

q[n_]:=q[n]=PrimeQ[n(n+1)-Prime[n]]&&PrimeQ[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, A232353, A235592, A235661, A235681, A235682, A235703, A235728.

Sequence in context: A129842 A065312 A343142 * A141337 A192187 A053403

Adjacent sequences:  A235724 A235725 A235726 * A235728 A235729 A235730

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, Jan 15 2014

STATUS

approved

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Last modified September 24 03:26 EDT 2021. Contains 347623 sequences. (Running on oeis4.)