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

1,1

Comments

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

Links

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

Example

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.

Mathematica

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

Crossrefs

Cf. A039650, A039651, A039652.

Sequence in context: A094779 A093387 A324408 * A195166 A225646 A225627

Adjacent sequences: A229484 A229485 A229486 * A229488 A229489 A229490

Keyword

nonn

Author

T. D. Noe, Oct 16 2013

Status

approved