

A100764


a(1) = 1, a(2) = 2, a(3) = 3, a(n) = least number not the sum of three or fewer previous terms.


1



1, 2, 3, 7, 13, 19, 25, 31, 37, 43, 49, 55, 61, 67, 73, 79, 85, 91, 97, 103, 109, 115, 121, 127, 133, 139, 145, 151, 157, 163, 169, 175, 181, 187, 193, 199, 205, 211, 217, 223, 229, 235, 241, 247, 253, 259, 265, 271, 277, 283, 289, 295, 301, 307, 313, 319, 325
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OFFSET

1,2


COMMENTS

Generalization: let the first k terms of the sequence be 1,2,...,k, and for n > k, let b(n) be defined as the least positive integer that is not the sum of k or fewer previous terms; then b(n+k) = b(n) + n* k(k+1)/2. b(n) = (n+1)*k*(k+1)/2 + 1. n > k. Here a(n) is for k=3.


LINKS

Table of n, a(n) for n=1..57.


FORMULA

a(n+4) = a(4) + 6n for n > 4; a(n) = 6n  17, n >3.
From Chai Wah Wu, Oct 25 2018: (Start)
a(n) = 2*a(n1)  a(n2) for n > 5.
G.f.: x*(2*x^4 + 3*x^3 + 1)/(x  1)^2. (End)


MATHEMATICA

a[1] = 1; a[2] = 2; a[3] = 3; a[n_] := a[n] = (m = 1; l = n  1; t = Union[ Flatten[ Join[ Table[ a[i], {i, l}], Table[ a[i] + a[j], {i, l}, {j, i + 1, l}], Table[ a[i] + a[j] + a[k], {i, l}, {j, i + 1, l}, {k, j + 1, l}] ]]]; While[ Position[t, m] != {}, m++ ]; m); Table[ a[n], {n, 60}] (* Robert G. Wilson v, Dec 14 2004 *)


CROSSREFS

Essentially the same as A016921.
Sequence in context: A105792 A130903 A068828 * A076974 A051484 A101415
Adjacent sequences: A100761 A100762 A100763 * A100765 A100766 A100767


KEYWORD

easy,nonn


AUTHOR

Amarnath Murthy, Nov 25 2004


EXTENSIONS

More terms from Robert G. Wilson v, Dec 14 2004


STATUS

approved



