A258435 Primes of form x^2 - phi(x) in increasing order.

3, 7, 43, 157, 1069, 1201, 4177, 4423, 5869, 6163, 8209, 17581, 19183, 22651, 26407, 37057, 48649, 60793, 61837, 82129, 89137, 102829, 113233, 115981, 121453, 141793, 143263, 190573, 208393, 230929, 283609, 292141, 303097, 314401, 337069

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

a(1) = 3, because  2^2 - 1 = 3, and 1^2 - 1 = 0 is not a prime.
a(2) = 7, since 3^2 = 9, phi(3) = 2, so 9-2 = 7 (prime).
a(3) = 43, since 7^2 = 49, phi(7) = 6, so 49-6 = 43 (prime).
a(6) = 1201, since 35^2 = 1225, phi(35) = 24, so 1225-24 = 1201 (prime).

Mathematica

lst = Table[n^2 - EulerPhi[n], {n, 1000}]; Select[lst, PrimeQ]
Select[Table[n^2 - EulerPhi[n], {n, 1000}], PrimeQ] (* Vincenzo Librandi, Jun 03 2015 *)

Prog

(Magma) [a: n in [1..1000] | IsPrime(a) where a is n^2-EulerPhi(n) ]; // Vincenzo Librandi, Jun 03 2015
(PARI) lista(nn) = {for (n=1, nn, if (isprime(p=n^2 -eulerphi(n)), print1(p, ", ")); ); } \\ Michel Marcus, Jul 08 2015

Crossrefs

Subset of A258434.

For phi see A000010.

A074268 is a subsequence. - Michel Marcus, Jun 19 2015

Cf. A259145.

Sequence in context: A050633 A107636 A303160 * A074268 A019026 A181729

Adjacent sequences: A258432 A258433 A258434 * A258436 A258437 A258438

Keyword

nonn,easy

Author

Carlos Eduardo Olivieri, May 30 2015

Extensions

More terms from Vincenzo Librandi, Jun 03 2015

Edited by Wolfdieter Lang, Jun 16 2015

Status

approved