A336881 a(n) is the number of solutions (x, m) of the generalized Ramanujan-Nagell equation x^2 + n = 2^m, x > 0, m > 0, n > 0.
1, 0, 1, 1, 0, 0, 5, 0, 0, 0, 0, 1, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 5, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1
Offset: 1
Keywords
Examples
1^2 + 1 = 2^1 hence a(1) = 1. 3^2 + 23 = 2^5 and 45^2 + 23 = 2^11 hence a(23) = 2. 28 = 2^5 - 2^2 = 2^6 - 6^2 = 2^7 - 10^2 = 2^9 - 22^2 = 2^17 - 362^2 hence a(28) = 5.
Links
- Roger Apéry, Sur une équation Diophantienne, C. R. Acad. Sci. Paris Sér. A251 (1960), 1263-1264.
- Frits Beukers, On the generalized Ramanujan-Nagell equation, I, Acta arithmetica, XXXVIII, 1980-1981, page 389-410.
- Wikipedia, Ramanujan-Nagell equation.
Extensions
More terms from Jinyuan Wang, Aug 07 2020
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