A258435 - OEIS

%I #26 Sep 08 2022 08:46:12

%S 3,7,43,157,1069,1201,4177,4423,5869,6163,8209,17581,19183,22651,

%T 26407,37057,48649,60793,61837,82129,89137,102829,113233,115981,

%U 121453,141793,143263,190573,208393,230929,283609,292141,303097,314401,337069

%N Primes of form x^2 - phi(x) in increasing order.

%H Amiram Eldar, <a href="/A258435/b258435.txt">Table of n, a(n) for n = 1..10000</a>

%e a(1) = 3, because  2^2 - 1 = 3, and 1^2 - 1 = 0 is not a prime.

%e a(2) = 7, since 3^2 = 9, phi(3) = 2, so 9-2 = 7 (prime).

%e a(3) = 43, since 7^2 = 49, phi(7) = 6, so 49-6 = 43 (prime).

%e a(6) = 1201, since 35^2 = 1225, phi(35) = 24, so 1225-24 = 1201 (prime).

%t lst = Table[n^2 - EulerPhi[n], {n, 1000}]; Select[lst, PrimeQ]

%t Select[Table[n^2 - EulerPhi[n], {n, 1000}], PrimeQ] (* _Vincenzo Librandi_, Jun 03 2015 *)

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

%o (PARI) lista(nn) = {for (n=1, nn, if (isprime(p=n^2 -eulerphi(n)), print1(p, ", ")););} \\ _Michel Marcus_, Jul 08 2015

%Y Subset of A258434.

%Y For phi see A000010.

%Y A074268 is a subsequence. - _Michel Marcus_, Jun 19 2015

%Y Cf. A259145.

%K nonn,easy

%O 1,1

%A _Carlos Eduardo Olivieri_, May 30 2015

%E More terms from _Vincenzo Librandi_, Jun 03 2015

%E Edited by _Wolfdieter Lang_, Jun 16 2015