A085554 Greater of twin primes of the form x^2+2, x^2+4.

5, 13, 229, 1093, 2029, 3253, 13693, 21613, 59053, 65029, 91813, 140629, 178933, 199813, 205213, 227533, 328333, 567013, 700573, 804613, 815413, 1071229, 2241013, 3629029, 4223029, 4347229, 4809253, 5212093, 5919493, 6185173

Offset: 1

Author

Cino Hilliard, Jul 04 2003

Keywords

• easy
• nonn

Comments

Except for the first term, all a(n)=13 (mod 72) with x=3 (mod 6). The lesser of the twin prime pair is given by A253639, the x-values in A086381. - M. F. Hasler, Jan 18 2015

Links

• M. F. Hasler, Table of n, a(n) for n = 1..3044 (all terms below 10^12).

Crossrefs

Cf. A085553, A086381, A087475, A059100.

Programs

Mathematica

Transpose[Select[Table[x^2+{2,4},{x,5000}],AllTrue[#,PrimeQ]&]][[2]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 15 2015 *)

PARI

is_A086381(x)=ispseudoprime(x^2+2)&&ispseudoprime(x^2+4) \\ or is_A067201(x)&&is_A007591(x)
A085554 = apply(A087475,select(is_A086381,vector(9999,n,n))) \\ A087475=x->x^2+4.
write(f="b085554.txt",c=1," 5"); forstep(x=3,1e6,6,is_A086381(x)&&write(f,c++" "x^2+4))
\\ M. F. Hasler, Jan 18 2015

Formula

A085554 = A087475 o A086381 = A020725^2 o A253639, i.e., a(n) = A087475(A086381(n)) = A253639(n)+2. - M. F. Hasler, Jan 18 2015

Extensions

Edited by Don Reble, May 03 2006

Definition corrected by Harvey P. Dale and Franklin T. Adams-Watters, Jan 15 2015