A116888 Primes p that remain prime through 4 iterations of the function f(p) = p^2 + 4.

306167, 48639197, 64695713, 68252687, 87788237, 87813293, 160486967, 255974437, 283032247, 324609913, 361705873, 417684523, 449364197, 451995587, 454052213, 466037563, 536504713, 574746467, 596095613

Offset

1,1

Links

Table of n, a(n) for n=1..19.

Example

p = 306167, f(p) = 93738231893, f(f(p)) = 8786856118425842363453, f(f(f(p))) = 77208840445917661077402487029419236950083213 and the 88-digit number f(f(f(f(p)))) are all prime numbers.

Mathematica

Select[Prime[Range[9! ]], PrimeQ[ #^2+4]&&PrimeQ[(#^2+4)^2+4]&&PrimeQ[((#^2+4)^2+4)^2+4]&&PrimeQ[(((#^2+4)^2+4)^2+4)^2+4]&] (* Vladimir Joseph Stephan Orlovsky, Feb 26 2010 *)
p4Q[p_]:=AllTrue[NestList[#^2+4&, p, 4], PrimeQ]; Select[Prime[Range[312*10^5]], p4Q] (* Harvey P. Dale, Nov 20 2023 *)

Crossrefs

Cf. A062324, A116886, A116887, A116889.

Sequence in context: A053849 A227780 A237950 * A270764 A236818 A234188

Adjacent sequences: A116885 A116886 A116887 * A116889 A116890 A116891

Keyword

nonn

Author

Giovanni Resta, Feb 27 2006

Status

approved