A003662 a(n) is smallest number != a(j) + a(k), j < k and a(1) = 1, a(2) = 4.

1, 4, 6, 8, 11, 13, 16, 18, 23, 25, 28, 30, 35, 37, 40, 42, 47, 49, 52, 54, 59, 61, 64, 66, 71, 73, 76, 78, 83, 85, 88, 90, 95, 97, 100, 102, 107, 109, 112, 114, 119, 121, 124, 126, 131, 133, 136, 138, 143, 145, 148, 150, 155, 157, 160, 162, 167, 169, 172, 174, 179, 181, 184

Offset: 1

Author

N. J. A. Sloane, Mira Bernstein

Keywords

• nonn
• easy

References

• R. K. Guy, "s-Additive sequences", preprint, 1994.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• R. K. Guy, s-Additive sequences, Preprint, 1994. (Annotated scanned copy)
• Aayush Rajasekaran, Using Automata Theory to Solve Problems in Additive Number Theory, MS thesis, University of Waterloo, 2018.
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Crossrefs

Cf. A060469.

Cf. A003666.

Programs

Mathematica

Sort[Join[{8},Select[Range[200],MemberQ[{1,4,6,11},Mod[#,12]]&]]] (* Harvey P. Dale, Apr 26 2011 *)

PARI

Vec(x*(2*x^8+x^6-x^5+2*x^4+2*x^3+2*x^2+3*x+1)/((x-1)^2*(x+1)*(x^2+1)) + O(x^100)) \\ Colin Barker, Feb 27 2015

Formula

Numbers congruent to {1, 4, 6, 11} mod 12 plus the number 8.

a(n) = a(n-1) + a(n-4) - a(n-5) for n > 7. - Colin Barker, Feb 27 2015

G.f.: x*(2*x^8 + x^6 - x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 3*x + 1) / ((x-1)^2*(x+1)*(x^2+1)). - Colin Barker, Feb 27 2015

Extensions

Name clarified by David A. Corneth, Mar 13 2023