A229487 Conjectured greatest number that converges to prime(n) under the iteration x -> phi(x) + 1, where phi is Euler's totient function.

2, 6, 12, 30, 22, 138, 60, 54, 46, 58, 62, 174, 498, 510, 94, 106, 118, 4314, 134, 142, 1038, 158, 166, 276, 420, 250, 206, 214, 750, 1758, 254, 262, 274, 278, 298, 302, 1182, 486, 334, 346, 358, 6360, 382, 1614, 394, 398, 422, 446, 454, 458, 5898, 478, 54582

Offset: 1

Author

T. D. Noe, Oct 16 2013

Keywords

• nonn

Comments

Many terms are just twice a prime: 6, 22, 46, 58, 62, 94,....

Examples

			The number 138 has trajectory {138, 45, 25, 21, 13}, which is conjecturally the last number that terminates with 13 = prime(6). Hence a(6) = 138.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A039650, A039651, A039652.

Programs

Mathematica

t = Table[NestWhileList[EulerPhi[#] + 1 &, n, UnsameQ, All][[-1]], {n, 100000}]; Table[Position[t, p][[-1]], {p, Prime[Range[53]]}]