A121834 Primes p of the form 4*n^2 + 1 such that 4*p^2+1 is also prime.

5, 37, 677, 1297, 2917, 8837, 13457, 50177, 147457, 156817, 246017, 341057, 414737, 746497, 1136357, 1726597, 1833317, 2119937, 2802277, 2808977, 3013697, 3549457, 3865157, 3896677, 4104677, 4384837, 5354597, 5410277, 5779217, 6031937, 6635777, 7001317

Offset

1,1

Comments

Intersection of A001912 and A121326. Except for the first term all other terms are == 7 (mod 10). Also all the primes 4*p^2+1 are == 7 (mod 10). - Zak Seidov, Mar 05 2015

Links

Table of n, a(n) for n=1..32.

Mathematica

fpQ[n_]:=PrimeQ[n]&&PrimeQ[4n^2+1]; Select[4Range[2000]^2+1, fpQ] (* Harvey P. Dale, Nov 07 2016 *)

Prog

(PARI) isA121834(n)={ if( (n-1) %4, return(0) ; ) ; if( issquare((n-1)/4), if( isprime(4*n^2+1), return(1), return(0) ), return(0) ; ) ; } { for(i=1, 1000000, p=prime(i) ; if( isA121834(p), print1(p, ", ") ; ) ; ) ; } /* R. J. Mathar, Sep 01 2006*/

Crossrefs

Cf. A002496, A052291, A121326.

Sequence in context: A246534 A095957 A354862 * A215233 A083846 A358887

Adjacent sequences: A121831 A121832 A121833 * A121835 A121836 A121837

Keyword

nonn

Author

Zak Seidov, Aug 28 2006

Extensions

More terms from R. J. Mathar, Sep 01 2006

Status

approved