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

1,1

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).

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

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 *)

Prog

(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

Crossrefs

Cf. A085553, A086381, A087475, A059100.

Sequence in context: A352083 A355763 A124878 * A226664 A067135 A122900

Adjacent sequences: A085551 A085552 A085553 * A085555 A085556 A085557

Keyword

easy,nonn

Author

Cino Hilliard, Jul 04 2003

Extensions

Edited by Don Reble, May 03 2006

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

Status

approved