

A083349


Least positive integers not appearing previously such that the selfconvolution cuberoot of this sequence consists entirely of integers.


5



1, 3, 6, 4, 9, 12, 7, 15, 18, 2, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 5, 54, 57, 10, 60, 63, 8, 66, 69, 72, 75, 78, 13, 81, 84, 87, 90, 93, 96, 99, 102, 16, 105, 108, 19, 111, 114, 11, 117, 120, 14, 123, 126, 22, 129, 132, 135, 138, 141, 25, 144, 147, 150, 153, 156, 28
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OFFSET

0,2


COMMENTS

A permutation of the positive integers. Positive integers congruent to 1 (mod 3) appear in ascending order at positions given by A106213. Positive integers congruent to 2 (mod 3) appear in ascending order at positions given by A106214. The selfconvolution cuberoot is A083350.


LINKS

Table of n, a(n) for n=0..66.
N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of nth Roots of Generating Functions, J. Combinatorial Theory, Series A, 113 (2006), 17321745.


EXAMPLE

The selfconvolution cube of A083350 equals this sequence: {1, 1, 1, 1, 3, 0, 6, 17, 17, 19, 114, ...}^3 = {1, 3, 6, 4, 9, 12, 7, 15, 18, ...}.
A083350(x)^3 = A(x) = 1 + 3x + 6x^2 + 4x^3 + 9x^4 + 12x^5 + 7x^6 + ...


MATHEMATICA

a[n_] := a[n] = Module[{A, P, t}, A = 1+3x; P = Table[0, 3(n+1)]; P[[1]] = 1; P[[3]] = 2; For[j = 2, j <= n, j++, For[k = 2, k <= 3(n+1), k++, If[P[[k]] == 0, t = Coefficient[(A + k x^j + x^2 O[x]^j)^(1/3), x, j]; If[Denominator[t] == 1, P[[k]] = j+1; A = A + k*x^j; Break[]]]]]; Coefficient[A + x O[x]^n, x, n]];
Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 0, 66}] (* JeanFrançois Alcover, Jul 25 2018, translated from PARI *)


PROG

(PARI) {a(n)=local(A=1+3*x, P=vector(3*(n+1))); P[1]=1; P[3]=2; for(j=2, n, for(k=2, 3*(n+1), if(P[k]==0, t=polcoeff((A+k*x^j+x^2*O(x^j))^(1/3), j); if(denominator(t)==1, P[k]=j+1; A=A+k*x^j; break)))); return(polcoeff(A+x*O(x^n), n))}


CROSSREFS

Cf. A106213, A106214, A083350, A106216.
Sequence in context: A336761 A143940 A321773 * A065230 A316478 A242224
Adjacent sequences: A083346 A083347 A083348 * A083350 A083351 A083352


KEYWORD

nonn


AUTHOR

Paul D. Hanna, Apr 25 2003; revised May 01 2005


STATUS

approved



