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