A125734 Primes of the form 4*3^k + 1.

5, 13, 37, 109, 2917, 19131877, 57395629, 16210220612075905069, 3187367866510497232065375864429355521950801431840733951694899540869109890815626195932616388528013, 254244997489062154119688681828370010268347235132197783249391539881181660045297550875174703528321187968562717038040968333

Offset

1,1

Comments

Venkataraman showed that, for every p of this form, 3p is a perfect totient number (cf. A082897).

References

Venkataraman, T. (1975). "Perfect totient number". The Mathematics Student 43: 178. MR0447089.

Links

Table of n, a(n) for n=1..10.

Paul Loomis, Michael Plytage and John Polhill, Summing up the Euler phi function, The College Mathematics Journal, Vol. 39, No. 1, Jan. 2008 (see Corollary 3).

Formula

4*3^n + 1 where n belongs to A005537.

Example

37 = 4*3^2 + 1 is a prime of this form. 973 = 4*3^5 + 1 = 7*139 is not a prime, so is not included in this sequence.

Mathematica

Do[p = 4*3^i + 1; If[PrimeQ@p, Print@p], {i, 0, 300}] (* Robert G. Wilson v, Feb 20 2007 *)

Crossrefs

Cf. A082897.

Sequence in context: A182312 A071100 A199108 * A146925 A146452 A146062

Adjacent sequences: A125731 A125732 A125733 * A125735 A125736 A125737

Keyword

nonn

Author

David Eppstein, Feb 06 2007, Feb 07 2007

Extensions

2 more terms from Robert G. Wilson v, Feb 20 2007

Status

approved