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

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

Offset: 1

Author

David Eppstein, Feb 06 2007, Feb 07 2007

Keywords

• nonn

Comments

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

Examples

			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.
		

References

• T. Venkataraman, Perfect totient number, The Mathematics Student, Vol. 43 (1975), p. 178. MR0447089.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..14
• Paul Loomis, Michael Plytage and John Polhill, Summing up the Euler phi function, The College Mathematics Journal, Vol. 39, No. 1 (Jan. 2008), pp. 34-42 (see Corollary 3).

Crossrefs

Cf. A005537, A082897.

Programs

Mathematica

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

Formula

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

Extensions

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