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

1,1

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

Links

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

Example

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).

Mathematica

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

Prog

(Magma) [n: n in [1..1000] | IsPrime(n^2 - EulerPhi(n))]; // Vincenzo Librandi, Jun 21 2015
(PARI) main(size)={ v=vector(size); i=0; m=1; while(i<size, if(isprime(m^2-eulerphi(m)), v[i++]=m); m++; ); return(v); } /* Anders Hellström, Jul 08 2015 */

Crossrefs

Cf. A000010, A003277, A065508, A258435.

Sequence in context: A324844 A007827 A250308 * A237255 A129859 A280765

Adjacent sequences: A259142 A259143 A259144 * A259146 A259147 A259148

Keyword

nonn,easy

Author

Carlos Eduardo Olivieri, Jun 19 2015

Status

approved