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
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
Programs
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Magma
[n: n in [1..1000] | IsPrime(n^2 - EulerPhi(n))]; // Vincenzo Librandi, Jun 21 2015
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Mathematica
Select[Range[2000], PrimeQ[#^2 - EulerPhi[#]] &]
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PARI
main(size)={ v=vector(size); i=0; m=1; while(i
Comments