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A140141
Positions of second appearances of primes in A039649.
8
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
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
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, May 10 2008
EXTENSIONS
Corrected and extended by Ray Chandler, May 20 2008
STATUS
approved