A262085 Numbers n such that phi(n + 8) = phi(n) + 8 where phi(n) = A000010(n) is Euler's totient function.

3, 5, 11, 23, 24, 29, 36, 42, 48, 50, 53, 56, 59, 71, 72, 80, 89, 101, 102, 125, 131, 132, 149, 173, 176, 191, 230, 233, 248, 263, 269, 359, 368, 389, 401, 431, 449, 464, 479, 491, 563, 569, 593, 599, 638, 653, 656, 683, 701, 719, 743, 761, 821, 848, 911, 929, 983

Offset: 1

Author

Kevin J. Gomez, Sep 10 2015

Keywords

• nonn
• easy

Comments

Sequence includes numbers n such that n and n + 8 are both prime (A023202).

Sequence also includes numbers n equal to 8*(a Mersenne prime) (cf A000668).

Sequence also includes n such that n/16 and n/8 + 1 are both odd primes.

Contains more composites than sequences A262084 and A262086. This is most likely due to the fact that 8 is a power of 2, as in A001838.

Examples

			3 since phi(11) = phi(3) + 8 (3 and 11 are both prime).
24 is a solution since phi(32) = phi(24) + 8 (24 is 8 * 3; 3 is a Mersenne prime).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Wikipedia, Euler's totient function

Crossrefs

Cf. A000010.

Cf. A001838 (k=2), A056772 (k=4), A262084 (k=6), A262086 (k=10).

Programs

Magma

[n: n in [1..1000] | EulerPhi(n+8) eq EulerPhi(n)+8]; // Vincenzo Librandi, Sep 11 2015

Maple

select(t -> numtheory:-phi(t+8) = numtheory:-phi(t)+8, [$1..1000]); # Robert Israel, Mar 04 2016

Mathematica

Select[Range@1000, EulerPhi@(# + 8)== EulerPhi[#] + 8 &] (* Vincenzo Librandi, Sep 11 2015 *)

PARI

is(n)=eulerphi(n + 8) == eulerphi(n) + 8 \\ Anders Hellström, Sep 11 2015

Sage

[n for n in (1..1000) if euler_phi(n+8) == euler_phi(n)+8] # Bruno Berselli, Mar 04 2016