A047332 Numbers that are congruent to {0, 2, 3, 5, 6} mod 7.

0, 2, 3, 5, 6, 7, 9, 10, 12, 13, 14, 16, 17, 19, 20, 21, 23, 24, 26, 27, 28, 30, 31, 33, 34, 35, 37, 38, 40, 41, 42, 44, 45, 47, 48, 49, 51, 52, 54, 55, 56, 58, 59, 61, 62, 63, 65, 66, 68, 69, 70, 72, 73, 75, 76, 77, 79, 80, 82, 83, 84, 86, 87, 89, 90, 91, 93, 94, 96, 97

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Melvyn B. Nathanson, On the fractional parts of roots of positive real numbers, Amer. Math. Monthly, 120 (2013), 409-429 [see p. 417].
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).

Programs

Mathematica

Floor[(7*Range[100] - 3)/5] (* Paolo Xausa, May 29 2025 *)

Formula

a(n) = a(n-5)+7. O.g.f.: x^2*(2+x+2*x^2+x^3+x^4)/((-1+x)^2*(x^4+x^3+x^2+x+1)). - R. J. Mathar, Apr 19 2008

a(n) = floor((7*n-3)/5). - Jason Yuen, May 27 2025