VOOZH about

URL: https://oeis.org/A262085

⇱ A262085 - OEIS

login
A262085
Numbers n such that phi(n + 8) = phi(n) + 8 where phi(n) = A000010(n) is Euler's totient function.
4
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
1,1
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.
EXAMPLE
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).
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 *)
PROG
(Magma) [n: n in [1..1000] | EulerPhi(n+8) eq EulerPhi(n)+8]; // Vincenzo Librandi, Sep 11 2015
(PARI) is(n)=eulerphi(n + 8) == eulerphi(n) + 8 \\ Anders Hellström, Sep 11 2015
(SageMath) [n for n in (1..1000) if euler_phi(n+8) == euler_phi(n)+8] # Bruno Berselli, Mar 04 2016
CROSSREFS
Cf. A000010.
Cf. A001838 (k=2), A056772 (k=4), A262084 (k=6), A262086 (k=10).
Sequence in context: A018110 A227806 A262431 * A015915 A275785 A106901
KEYWORD
nonn,easy
AUTHOR
Kevin J. Gomez, Sep 10 2015
STATUS
approved