A006596 Numbers k such that (2^(2k+1) - 2^(k+1) + 1)/5 is prime.

2, 5, 6, 14, 21, 26, 141, 278, 281, 306, 345, 1365, 2573, 2661, 4766, 5385

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• hard
• more

References

• J. Brillhart et al., Factorizations of b^n +- 1. Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 2nd edition, 1985; and later supplements.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
• Victor Meally, Letter to N. J. A. Sloane, no date.
• S. S. Wagstaff, Jr., The Cunningham Project

Programs

Mathematica

For[ i=1, i<=10000, i++, If[ PrimeQ[ ( 2^(2n+1) - 2^(n+1) + 1)/5 ], Print[ n ] ] ]
Select[Range[5400],PrimeQ[(2^(2#+1)-2^(#+1)+1)/5]&] (* Harvey P. Dale, Jun 28 2023 *)

PARI

is(n)=ispseudoprime((2^(2*n+1) - 2^(n+1) + 1)/5) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

More terms from Douglas R. Burke (dburke(AT)nevada.edu)