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

1,2

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).

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)

Mathematica

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

Prog

(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

Crossrefs

Cf. A026476, A026474.

Sequence in context: A081256 A084955 A273056 * A286176 A318401 A322703

Adjacent sequences: A026469 A026470 A026471 * A026473 A026474 A026475

Keyword

nonn

Author

Clark Kimberling

Extensions

More terms from Clark Kimberling, Oct 10 2019

Status

approved