A026472 {3, 7} together with the numbers congruent to {1, 2} mod 12.

1, 2, 3, 7, 13, 14, 25, 26, 37, 38, 49, 50, 61, 62, 73, 74, 85, 86, 97, 98, 109, 110, 121, 122, 133, 134, 145, 146, 157, 158, 169, 170, 181, 182, 193, 194, 205, 206, 217, 218, 229, 230, 241, 242, 253, 254, 265, 266, 277, 278, 289, 290, 301, 302, 313, 314

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Comments

The old definition of this sequence was "a(n) = least positive integer > a(n-1) and not equal to a(i)+a(j)+a(k) for 1<=i<=j<=k<=n". However, Ralf Stephan observes that this does not fit the terms shown. The present definition (due to Stephan) has been adopted as a temporary solution. - N. J. A. Sloane, Nov 24 2004

Regarding the old definition, see Comments at A047239. - Clark Kimberling, Oct 09 2019

Links

• Clark Kimberling, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Crossrefs

Cf. A026476, A026474.

Programs

Mathematica

p = {1, 2, 3, 7}; r = 12 Range[200]; Union[p, 1 + r, 2 + r] (* Clark Kimberling, Oct 10 2019 *)

PARI

Vec(x*(1 + x + 3*x^3 + 5*x^4 - 3*x^5 + 5*x^6) / ((1 - x)^2*(1 + x)) + O(x^40)) \\ Colin Barker, Oct 20 2019

Formula

From Colin Barker, Oct 10 2019: (Start)

G.f.: x*(1 + x + 3*x^3 + 5*x^4 - 3*x^5 + 5*x^6) / ((1 - x)^2*(1 + x)).

a(n) = a(n-1) + a(n-2) - a(n-3) for n>6.

a(n) = -(39/2) - (5*(-1)^n)/2 + 6*n for n>4.

(End)

Extensions

More terms from Clark Kimberling, Oct 10 2019