A218862 The least number having n representations as p*q - p - q for primes p <= q.

2, 0, 3, 35, 71, 1151, 1079, 4199, 11879, 7559, 32759, 30239, 75599, 171359, 241919, 251999, 262079, 393119, 604799, 665279, 1572479, 1834559, 2827439, 2570399, 2358719, 7862399, 7814015, 5405399, 6683039, 18017999, 20180159, 8648639, 17992799, 17297279

Offset

0,1

Comments

a(72) > 2^32. - Donovan Johnson, Dec 07 2012

Links

Donovan Johnson, Table of n, a(n) for n = 0..71

Example

The values of a(n) and (p,q) for n = 1 to 6:
0 is    (2,2).
3 is    (2,5),    (3,3).
35 is   (2,37),   (3,19),  (7,7).
71 is   (2,73),   (3,37),  (5,19),  (7,13).
1151 is (2,1153), (3,577), (7,193), (13,97),  (17,73).
1079 is (3,541),  (5,271), (7,181), (11,109), (19,61), (31,37).

Mathematica

nn = 10000; ps = Prime[Range[PrimePi[nn + 1]]]; t = Table[0, {nn}]; Do[n = p*q - p - q; If[p <= q && 0 < n <= nn, t[[n]]++], {p, ps}, {q, ps}]; t = Join[{1}, t]; u = Union[t]; c = Complement[Range[Max[u]], u]; If[c == {}, mx = u[[-1]], mx = c[[-1]] - 1]; Table[Position[t, n, 1, 1][[1, 1]] - 1, {n, 0, mx}]

Crossrefs

Cf. A157187.

Sequence in context: A223706 A347034 A261162 * A243199 A305212 A104774

Adjacent sequences: A218859 A218860 A218861 * A218863 A218864 A218865

Keyword

nonn

Author

T. D. Noe, Dec 06 2012

Status

approved