A140141 - OEIS

%I #18 Jan 14 2017 07:56:24

%S 2,4,8,9,22,21,32,27,46,58,62,57,55,49,94,106,118,77,134,142,91,158,

%T 166,115,119,125,206,214,133,145,254,262,274,278,298,302,169,243,334,

%U 346,358,209,382,221,394,398,422,446,454,458,295,478,287,502,512,526,538

%N Positions of second appearances of primes in A039649.

%C The first occurrence of a prime p in A039649 is not interesting because for an odd prime p it is evidently p.

%C Since phi(p) = phi(2p) = p-1 for odd prime p, then for n > 1 we have prime(n) < a(n) <= 2*prime(n).

%C For n > 1, a(n) is the smallest composite k such that phi(k) = prime(n)-1. - _Thomas Ordowski_, Jan 02 2017

%C If prime(n) > 7 is in A005385, then a(n) = 2*prime(n). - _Thomas Ordowski_ (conjecture) and _Robert Israel_ (proof), Jan 04 2017

%H Michael De Vlieger, <a href="/A140141/b140141.txt">Table of n, a(n) for n = 1..10000</a>

%t Table[Function[p, First@ Drop[Lookup[#, p], 1]]@ Prime@ n, {n, 57}] &@ PositionIndex@ Table[EulerPhi@ n + 1, {n, 10^5}] (* _Michael De Vlieger_, Jan 02 2017, Version 10 *)

%Y Cf. A000010, A000040, A039649.

%K nonn

%O 1,1

%A _Vladimir Shevelev_, May 10 2008

%E Corrected and extended by _Ray Chandler_, May 20 2008