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 A083349 Least positive integers not appearing previously such that the self-convolution cube-root 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 (list; graph; refs; listen; history; text; internal format)
 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 self-convolution cube-root is A083350. LINKS N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745. EXAMPLE The self-convolution 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}] (* Jean-François 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

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Last modified November 29 18:41 EST 2021. Contains 349416 sequences. (Running on oeis4.)