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A258435 Primes of form x^2 - phi(x) in increasing order. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 12 14:45 EDT 2021. Contains 344957 sequences. (Running on oeis4.)