A160524 Exceptional class of numbers k such that p(5k+4) == 0 (mod 25), where p() = A000041().

8, 15, 17, 37, 41, 46, 51, 53, 55, 65, 75, 77, 102, 106, 110, 116, 130, 131, 138, 140, 147, 157, 158, 165, 166, 167, 178, 180, 183, 192, 197, 217, 222, 225, 233, 235, 251, 258, 285, 287, 302, 310, 315, 321, 325, 328, 333, 336, 340, 355, 368, 371, 377, 380, 393, 416, 418, 420, 430, 432, 441, 447

Offset: 1

Author

N. J. A. Sloane, Nov 13 2009

Keywords

• nonn

Comments

The unexceptional class consists of the numbers k == 4 (mod 5).

(p(5*a(m) + 4)/25: m >= 1) = (3007, 553946, 1999837, 61090943985, 341143252095, 2634063438811, 18381830017947, 38993374797785, 81633034103003, ...) - Petros Hadjicostas, Sep 23 2019

Links

• Watson, G. N., Ramanujans Vermutung über Zerfällungsanzahlen, J. Reine Angew. Math. (Crelle) 179 (1938), 97-128; see p. 113.

Crossrefs

Cf. A000041, A071734, A327713, A327714.

Programs

Maple

isA160524 := n -> 0 = modp(combinat:-numbpart(5*n + 4), 25) and 4 <> modp(n, 5):
select(isA160524, [$1..200]); # Petros Hadjicostas, Sep 23 2019

Extensions

More terms from Petros Hadjicostas, Sep 23 2019