A002257 Numbers k such that 13*4^k + 1 is prime.
1, 4, 5, 10, 14, 41, 94, 154, 158, 500, 14140, 19004, 21928, 44009, 54629, 57148, 260653, 281228, 342280, 519448, 749938, 930866
Offset: 1
References
- H. Riesel, "Prime numbers and computer methods for factorization," Progress in Mathematics, Vol. 57, Birkhauser, Boston, 1985, Chap. 4, see pp. 381-384.
- N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Links
- Ray Ballinger, Proth Search Page.
- R. M. Robinson, A report on primes of the form k.2^n+1 and on factors of Fermat numbers, Proc. Amer. Math. Soc., 9 (1958), 673-681.
Crossrefs
See A032356 (n such that 13*2^n+1 is prime) for more terms.
Programs
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Magma
[ k: k in [1..800]|IsPrime(13*4^k+1)]; // Vincenzo Librandi, Nov 21 2010
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Mathematica
Select[Range[2000],PrimeQ[13 4^#+1]&] (* Harvey P. Dale, Jan 22 2011 *)
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PARI
for(k=1,10^5,if(ispseudoprime(13*4^k+1),print1(k, ", "))); /* Joerg Arndt, Apr 07 2013 */
Extensions
Added more terms (from A032356), Joerg Arndt, Apr 07 2013