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A212287 Primes of the form m*p^2 + 1, where p is prime and m <= p^2. 1
5, 13, 17, 19, 37, 73, 101, 151, 197, 251, 401, 491, 601, 677, 727, 883, 1373, 1453, 1471, 1667, 2029, 2179, 2663, 3389, 3469, 3631, 3719, 4057, 4357, 4733, 5477, 6359, 6761, 7019, 8093, 8713, 8837, 9127, 9439, 9803, 9923, 10093, 10141, 10831, 10891, 11617, 11831, 12101, 12343 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Not known to be infinite, but see the Matomäki link.

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Kaisa Matomäki, A note on primes of the form p = aq^2 + 1, Acta Arith. 137 (2009), pp. 133-137.

EXAMPLE

13 is a member since 13 = 3 * 2^2 + 1 with 3 <= 2^2 and 3 is prime.

PROG

(PARI) list(lim)=my(v=List(), t); lim=lim\1-.5; forprime(p=2, sqrt(lim), for(a=1, min(lim\p^2, p^2), if(isprime(t=a*p^2+1), listput(v, t)))); vecsort(Vec(v), , 8)

CROSSREFS

Cf. A028916, A173587.

Sequence in context: A049092 A103666 A082700 * A174361 A226165 A166409

Adjacent sequences:  A212284 A212285 A212286 * A212288 A212289 A212290

KEYWORD

nonn

AUTHOR

Charles R Greathouse IV, Jun 13 2012

STATUS

approved

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Last modified June 26 00:10 EDT 2019. Contains 324367 sequences. (Running on oeis4.)