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

Author

Carlos Eduardo Olivieri, May 30 2015

Keywords

• nonn
• easy

Examples

			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).
		

Links

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

Crossrefs

Subset of A258434.

For phi see A000010.

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

Cf. A259145.

Programs

Magma

[a: n in [1..1000] | IsPrime(a) where a is n^2-EulerPhi(n) ]; // Vincenzo Librandi, Jun 03 2015

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 *)

PARI

lista(nn) = {for (n=1, nn, if (isprime(p=n^2 -eulerphi(n)), print1(p, ", ")););} \\ Michel Marcus, Jul 08 2015

Extensions

More terms from Vincenzo Librandi, Jun 03 2015

Edited by Wolfdieter Lang, Jun 16 2015