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A227083 Number of ways to write n as a + b/2 with a and b terms of the sequence A008407. 2
0, 0, 1, 0, 1, 1, 1, 1, 2, 2, 1, 3, 1, 2, 2, 3, 2, 3, 2, 3, 3, 3, 3, 4, 1, 4, 4, 2, 3, 5, 3, 4, 5, 4, 3, 7, 4, 4, 3, 6, 5, 5, 3, 6, 5, 6, 4, 6, 4, 6, 7, 5, 5, 7, 4, 6, 6, 7, 4, 7, 6, 5, 8, 5, 6, 9, 6, 5, 6, 7, 8, 8, 6, 7, 7, 9, 7, 7, 5, 9, 10, 6, 8, 9, 8, 10, 7, 8, 7, 11, 8, 7, 9, 9, 10, 10, 8, 9, 8, 13 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,9

COMMENTS

Conjecture: We have a(n) > 0 for all n > 4.

For every k = 2, ..., 342, the value of A008407(k) has been determined by T. J. Engelsma. Since A008407(343)/2 >  A008407(342)/2 = 2328/2 = 1164,  if n <= 1166 can be written as  A008407(j) + A008407(k)/2 with j > 1 and k > 1 then neither j nor k exceeds 342. Based on this we are able to compute a(n) for n = 1, ..., 1166.

LINKS

Zhi-Wei Sun, Table of n, a(n) for n = 1..1166

A. V. Sutherland, Narrow admissible k-tuples: bounds on H(k), 2013.

T. Tao, Bounded gaps between primes, PolyMath Wiki Project, 2013.

EXAMPLE

a(10) = 2 since 10 = 2 + 16/2 = 6 + 8/2;

a(11) = 1 since 11 = 8 + 6/2;

a(25) = 1 since 25 = 12 + 26/2.

CROSSREFS

Cf. A008407.

Sequence in context: A238882 A135352 A072528 * A166363 A117470 A070786

Adjacent sequences:  A227080 A227081 A227082 * A227084 A227085 A227086

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, Jun 30 2013

STATUS

approved

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Last modified December 5 19:19 EST 2016. Contains 278770 sequences.