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A283532 Primes p such that (q^2 - p^2) / 24 is prime, where q is the next prime after p. 2
7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 67, 83, 101, 109, 127, 131, 137, 251, 271, 281, 307, 331, 379, 383, 443, 487, 499, 563, 617, 641, 769, 821, 877, 937, 971, 1009, 1123, 1223, 1231, 1283, 1291, 1297, 1543, 1567, 1697, 1877, 2063, 2081, 2237, 2269, 2371, 2381, 2383, 2389, 2551, 2657, 2659, 2801, 2851, 2857 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This sequence is union of primes of the form:

6t-1 such that 6t+1 and t are both prime,

6t-1 such that 6t+5 and 3t+1 are both prime and 6t+1 is composite,

6t+1 such that 6t+5 and 2t+1 are both prime,

6t+1 such that 6t+7 and 3t+2 are both prime and 6t+5 is composite.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

7 is a term since 11 is the next prime and (11^2 - 7^2)/24 = 3 is prime.

MAPLE

N:= 10000: # to get all terms <= N

Primes:= select(isprime, [seq(i, i=3..N, 2)]):

f:= proc(p, q)

  local r;

  r:= (q^2-p^2)/24;

  if r::integer and isprime(r) then p fi

end proc:

seq(f(Primes[i], Primes[i+1]), i=1..nops(Primes)-1); # Robert Israel, Mar 10 2017

MATHEMATICA

Select[Prime@ Range@ 415, PrimeQ[(NextPrime[#]^2 - #^2)/24] &] (* Michael De Vlieger, Mar 13 2017 *)

PROG

(PARI) is(n) = n>3 && isprime(n) && isprime((nextprime(n+1)^2-n^2)/24);

CROSSREFS

A060213 is a subsequence.

Cf. A075888.

Sequence in context: A020633 A078873 A020603 * A163648 A135776 A067831

Adjacent sequences:  A283529 A283530 A283531 * A283533 A283534 A283535

KEYWORD

nonn

AUTHOR

Thomas Ordowski and Altug Alkan, Mar 10 2017

STATUS

approved

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Last modified January 25 07:57 EST 2020. Contains 331241 sequences. (Running on oeis4.)