A227156 - OEIS

%I #10 Jul 03 2013 19:24:09

%S 1,1,1,2,2,1,2,2,1,3,1,2,2,2,2,2,4,1,4,2,1,4,0,3,4,3,1,3,4,2,3,2,3,4,

%T 2,1,4,2,4,4,3,4,2,4,1,5,2,1,5,3,5,2,2,4,3,3,3,3,3,3,4,1,3,5,4,4,4,2,

%U 4,4,3,4,3,6,1,3,5,2,6,4,3,7,2,4,6,2,3,5,5,2,4,4,4,6,4,3,5,3,5,3

%N Number of ways to write n as a sum of a square and half of a term of the sequence A008407

%C Conjecture: We have a(n) > 0  except for n = 23.

%C We also conjecture that any positive integer can be written as a sum of a triangular number and half of a term of A008407, and each integer n > 4 can be written as x + y (x>0, y>0) with x*y a term of A008407.

%H Zhi-Wei Sun, <a href="/A227156/b227156.txt">Table of n, a(n) for n = 1..1164</a>

%H A. V. Sutherland, <a href="http://math.mit.edu/~primegaps">Narrow admissible k-tuples: bounds on H(k)</a>, 2013.

%H T. Tao, <a href="http://michaelnielsen.org/polymath1/index.php?title=Bounded_gaps_between_primes">Bounded gaps between primes</a>, PolyMath Wiki Project, 2013.

%e a(195) = 1 since 195 = 0^2 + A008407(23)/2.

%e a(378) = 1 since 378 = 8^2 + A008407(110)/2.

%Y Cf. A000290, A008407, A227083.

%K nonn

%O 1,4

%A _Zhi-Wei Sun_, Jul 02 2013