A248375 a(n) = floor(9*n/8).

0, 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 61, 63, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95

Offset: 0

Author

M. F. Hasler, Oct 05 2014

Keywords

• nonn
• easy

Comments

Also: numbers not congruent to 8 (mod 9), or numbers whose base-9 expansion does not end in the digit "8".

Paz proves that for all n>0 there is a prime in Breusch's interval [n; a(n+3)], cf A248371.

Links

• G. A. Paz, On the Interval [n; 2n]: Primes, Composites and Perfect Powers, Gen. Math. Notes 15 no. 1 (2013), 1-15.
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,1,-1).

Crossrefs

Cf. A032766, A004773, A001068, A047226, A047368, A004777, A168183, A281899 (subsequence).

Programs

Magma

[Floor(9*n/8): n in [0..90]]; // Bruno Berselli, Oct 06 2014

Mathematica

Table[Floor[9 n/8], {n, 0, 90}] (* Bruno Berselli, Oct 06 2014 *)

PARI

a(n)=9*n\8

Formula

G.f.: x*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + 2*x^7) / ((1 + x)*(1 - x)^2*(1 + x^2)*(1 + x^4)). [Bruno Berselli, Oct 06 2014]

a(n) = n + floor(n/8) = a(n-1) + a(n-8) - a(n-9). [Bruno Berselli, Oct 06 2014]

a(n) = A168183(n+1) - 1. - Philippe Deléham, Dec 05 2013