A000068 Numbers k such that k^4 + 1 is prime.
1, 2, 4, 6, 16, 20, 24, 28, 34, 46, 48, 54, 56, 74, 80, 82, 88, 90, 106, 118, 132, 140, 142, 154, 160, 164, 174, 180, 194, 198, 204, 210, 220, 228, 238, 242, 248, 254, 266, 272, 276, 278, 288, 296, 312, 320, 328, 334, 340, 352, 364, 374, 414, 430, 436, 442, 466
Offset: 1
References
- Harvey Dubner, Generalized Fermat primes, J. Recreational Math., 18 (1985): 279-280.
- 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
- T. D. Noe, Table of n, a(n) for n = 1..10000
- R. K. Guy, The strong law of small numbers. Amer. Math. Monthly 95 (1988), no. 8, 697-712. [Annotated scanned copy]
- M. Lal, Primes of the form n^4 + 1, Math. Comp., 21 (1967), 245-247.
- D. Shanks, On numbers of the form n^4+1, Math. Comp. 15 (74) (1961), 186-189.
Crossrefs
Programs
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Magma
[n: n in [0..800] | IsPrime(n^4+1)]; // Vincenzo Librandi, Nov 18 2010
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Mathematica
Select[Range[10^2*2], PrimeQ[ #^4+1] &] (* Vladimir Joseph Stephan Orlovsky, May 01 2008 *)
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PARI
{a(n) = local(m); if( n<1, 0, for(k=1, n, until( isprime(m^4 + 1), m++)); m)}; -
PARI
list(lim)=my(v=List([1])); forstep(k=2,lim,2, if(isprime(k^4+1), listput(v,k))); Vec(v) \\ Charles R Greathouse IV, Mar 31 2022
Formula
1+a(n)^4 = A037896(n).