A076947 Smallest k > 0 such that nk+1 is a cube.
7, 13, 21, 31, 43, 57, 1, 91, 7, 133, 157, 183, 2, 52, 273, 307, 343, 19, 18, 463, 3, 553, 601, 651, 703, 1, 37, 26, 931, 993, 4, 1123, 1191, 1261, 38, 61, 27, 9, 105, 1723, 1807, 372, 5, 2071, 91, 2257, 2353, 2451, 119, 2653, 2757, 14, 2971, 127, 3193, 13, 6, 3541
Offset: 1
Keywords
References
- Dorin Andrica, Vlad Crişan, The smallest nontrivial solution to x^k == 1 (mod n) ..., Amer. Math. Monthly 126 (2019), 173-178.
Links
- Robert G. Wilson v, Table of n, a(n) for n = 1..1000
Programs
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Mathematica
Do[k = 1; While[ !IntegerQ[(n*k + 1)^(1/3)], k++ ]; Print[k], {n, 1, 58}] f[n_] := Block[{x = 2}, While[ Mod[x^3 - 1, n] != 0, x++]; (x^3 - 1)/n]; Array[f, 58] (* Robert G. Wilson v, Mar 29 2016 *) -
PARI
a(n) = my(k = 1); while(! ispower(n*k+1, 3), k++); k; \\ Michel Marcus, Mar 30 2016
Extensions
Edited and extended by Robert G. Wilson v, Oct 21 2002