A140141 Positions of second appearances of primes in A039649.

2, 4, 8, 9, 22, 21, 32, 27, 46, 58, 62, 57, 55, 49, 94, 106, 118, 77, 134, 142, 91, 158, 166, 115, 119, 125, 206, 214, 133, 145, 254, 262, 274, 278, 298, 302, 169, 243, 334, 346, 358, 209, 382, 221, 394, 398, 422, 446, 454, 458, 295, 478, 287, 502, 512, 526, 538

Offset: 1

Author

Vladimir Shevelev, May 10 2008

Keywords

• nonn

Comments

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

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

For n > 1, a(n) is the smallest composite k such that phi(k) = prime(n)-1. - Thomas Ordowski, Jan 02 2017

If prime(n) > 7 is in A005385, then a(n) = 2*prime(n). - Thomas Ordowski (conjecture) and Robert Israel (proof), Jan 04 2017

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A000040, A039649.

Programs

Mathematica

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 *)

Extensions

Corrected and extended by Ray Chandler, May 20 2008