A249749 Primes p such that phi(p - k) = phi(p + k) has no solution, where phi is A000010.

2, 3, 7, 13, 19, 43, 53, 59, 79, 89, 97, 109, 127, 131, 151, 173, 251, 269, 281, 311, 359, 443, 449, 479, 521, 547, 631, 647, 857, 883, 929, 941, 991, 1123, 1187, 1217, 1327, 1429, 1847, 1999, 2137, 2267, 2297, 2371, 2423, 2803

Offset

1,1

Comments

a(66) = 39383, then there are no more terms up to 10^7. - Charles R Greathouse IV, Nov 08 2014

Is 5 the only solution to phi(n) = phi(n-k) + phi(n+k)? - Jon Perry, Nov 08 2014

Links

Amiram Eldar, Table of n, a(n) for n = 1..66

Example

5 is not in this sequence because phi(5 - 1) = phi(5 + 1) = 2,
11 is not in this sequence because phi(11 - 1) = phi(11 + 1) = 4,
17 is not in this sequence because phi(17 - 4) = phi(17 + 4) = 12.

Mathematica

aQ[p_] := PrimeQ[p] && AllTrue[Range[p + 1, 2 p - 1], EulerPhi[2p - #] != EulerPhi[#] &]; Select[Range[40000], aQ] (* Amiram Eldar, Jul 11 2019 *)

Prog

(PARI) is(n)=forcomposite(c=n+1, 2*n-1, if(eulerphi(c)==eulerphi(2*n-c), return(0))); isprime(n) \\ Charles R Greathouse IV, Nov 06 2014

Crossrefs

Cf. A000010 (Euler totient function).

Sequence in context: A319496 A038940 A019383 * A171817 A156300 A067834

Adjacent sequences: A249746 A249747 A249748 * A249750 A249751 A249752

Keyword

nonn,fini

Author

Juri-Stepan Gerasimov, Nov 04 2014

Status

approved