A259145 Numbers k such that k^2 - phi(k) is prime, where phi() is A000010.

2, 3, 7, 13, 33, 35, 65, 67, 77, 79, 91, 133, 139, 151, 163, 193, 221, 247, 249, 287, 299, 321, 337, 341, 349, 377, 379, 437, 457, 481, 533, 541, 551, 561, 581, 591, 595, 611, 613, 643, 721, 727, 763, 769, 779, 789, 803, 817, 843, 851, 869, 917, 919, 991

Offset: 1

Author

Carlos Eduardo Olivieri, Jun 19 2015

Keywords

• nonn
• easy

Comments

Conjecture: a(n) is a cyclic number (see A003277) for all n.

A065508 is the subsequence of prime terms. - Michel Marcus, Jun 19 2015

Examples

			a(1) = 2, since phi(2) = 1, thus 2^2 - 1 = 3 (prime).
a(3) = 7, since phi(7) = 6, thus 7^2 - 6 = 43 (prime).
a(5) = 33, since phi(33) = 20, thus 33^2 - 20 = 1069 (prime).
		

Links

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

Crossrefs

Cf. A000010, A003277, A065508, A258435.

Programs

Magma

[n: n in [1..1000] | IsPrime(n^2 - EulerPhi(n))]; // Vincenzo Librandi, Jun 21 2015

Mathematica

Select[Range[2000], PrimeQ[#^2 - EulerPhi[#]] &]

PARI

main(size)={ v=vector(size); i=0; m=1; while(iAnders Hellström, Jul 08 2015 */