The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A051154 a(n) = 1 + 2^k + 4^k where k = 3^n. 8
 7, 73, 262657, 18014398643699713, 5846006549323611672814741748716771307882079584257 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS The first three terms are prime. Are there more? Golomb shows that k must be a power of 3 in order for 1 + 2^k + 4^k to be prime. - T. D. Noe, Jul 16 2008 The next term, a(5) has 147 digits and is too large to include in DATA. - David A. Corneth, Aug 19 2020 LINKS Jeppe Stig Nielsen, Table of n, a(n) for n = 0..6 D. Alpern, Factors of Generalized Fermat Numbers Walter Feit, Finite projective planes and a question about primes, Proc. AMS, Vol. 108(1990), 561-564. Solomon W. Golomb, Cyclotomic polynomials and factorization theorems, Amer. Math. Monthly 85 (1978), 734-737. FORMULA a(n) = (2^(3^(n+1))-1)/(2^(3^n)-1). MAPLE with(numtheory); F := proc(n, r) local p; p := ithprime(r); (2^(p^(n+1))-1)/(2^(p^n)-1); end; [ seq(F(n, 2), n=0..5) ]; MATHEMATICA Table[4^(3^n) + 2^(3^n) + 1, {n, 1, 5}]  (* Artur Jasinski, Oct 31 2011 *) PROG (PARI) a(n)=1+2^3^n+4^3^n \\ Charles R Greathouse IV, Oct 31 2011 CROSSREFS Cf. A001576, A051155, A051156, A051157. Sequence in context: A134281 A215612 A292012 * A172257 A106427 A106417 Adjacent sequences:  A051151 A051152 A051153 * A051155 A051156 A051157 KEYWORD nonn,easy AUTHOR STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 21 13:00 EDT 2020. Contains 337272 sequences. (Running on oeis4.)