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A063500 a(n) is the least composite solution of phi(k + 6n) = phi(k) + 6n. 3

%I #22 Dec 19 2021 09:24:08

%S 21,45,63,95,224,135,301,95,189,161,260,115,400,165,476,195,620,145,

%T 644,203,640,285,343,155,728,185,567,155,560,301,860,185,1000,329,

%U 1892,235

%N a(n) is the least composite solution of phi(k + 6n) = phi(k) + 6n.

%C Next term (a(37)) exceeds 10^5. - _Matthew Conroy_, Sep 13 2001

%C Next term (a(37)), if it exists, exceeds 10^7. - _David Wasserman_, Jul 03 2002

%C If a(37) exists, it is larger than 7.6 * 10^11. - _Jud McCranie_, Aug 29 2013

%C a(37) > 10^13, if it exists. - _Giovanni Resta_, Feb 25 2020

%F Smallest values satisfying A000010(a(n)+6n)=A000010(a(n))+6n relation.

%e n=100, d=600=6n, a(100)=671=11*61, phi(671)=600, phi(671+600)=phi(1271)=(31-1)*(41-1)=600+600=phi(671)+d.

%o (PARI) for (n=1, 36, a=1; while (isprime(a) || eulerphi(a + 6*n) != eulerphi(a) + 6*n, a++); write("b063500.txt", n, " ", a) ) \\ _Harry J. Smith_, Aug 24 2009

%Y Cf. A000010, A054904, A054905.

%K nonn,more

%O 1,1

%A _Labos Elemer_, Jul 30 2001

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Last modified March 29 08:01 EDT 2024. Contains 371265 sequences. (Running on oeis4.)