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

1,1

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

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 *)

Crossrefs

Cf. A000010, A000040, A039649.

Sequence in context: A177404 A046685 A248741 * A088274 A118418 A074810

Adjacent sequences: A140138 A140139 A140140 * A140142 A140143 A140144

Keyword

nonn

Author

Vladimir Shevelev, May 10 2008

Extensions

Corrected and extended by Ray Chandler, May 20 2008

Status

approved