

A109136


Even numbers that are not congruent to 1 mod 3 nor are squares nor are the sum of a prime and a square of a prime.


1



2, 8, 18, 24, 74, 170, 614, 704, 1010, 1164, 15054, 21774, 24476
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

We conjecture that every sufficiently large even number is congruent to 1 mod 3, or is a square, or is a sum of a prime and a square of a prime. The numbers listed here are believed to be the only exceptions. This has been verified up to 100000000.


LINKS



MATHEMATICA

okQ[n_]:=Mod[n, 3]!=1&&!IntegerQ[Sqrt[n]]&&Count[nPrime[Range[ PrimePi[n]]], _?(PrimeQ[Sqrt[#]]&)]==0; Select[Range[0, 25000, 2], okQ] (* Harvey P. Dale, Nov 08 2012 *)


CROSSREFS



KEYWORD

nonn


AUTHOR

Dmytro Taranovsky (dmytro(AT)mit.edu), Aug 17 2005


STATUS

approved



