A132841 Least increasing logarithmic coefficients such that exponentiation results in an integer sequence (A132842), starting with a(1)=1.

1, 3, 4, 7, 11, 12, 15, 23, 31, 33, 34, 40, 53, 59, 74, 87, 103, 111, 115, 117, 123, 124, 139, 152, 161, 185, 193, 203, 204, 222, 249, 279, 301, 309, 340, 355, 371, 383, 407, 413, 452, 467, 474, 480, 506, 509, 518, 552, 554, 583, 616, 657, 690, 705, 759, 779

Offset

1,2

Links

Table of n, a(n) for n=1..56.

Example

L.g.f.: A(x) = x + 3x^2/2 + 4x^3/3 + 7x^4/4 + 11x^5/5 + 12x^6/6 + 15x^7/7 +...
exp(A(x)) = 1 + x + 2x^2 + 3x^3 + 5x^4 + 8x^5 + 12x^6 + 18x^7 +...(A132842).

Prog

(PARI) {a(n)=local(A, t, r=1); A=if(n==1, [1], vector(n-1, j, a(j)/j)); if(n==1, r=1, for(j=1, n, if(denominator(Vec(exp(x*Ser(concat(A, (a(n-1)+j)/n))))[n+1])==1, r=a(n-1)+j; j=n+1))); r}

Crossrefs

Cf. A132842.

Sequence in context: A291063 A047543 A030489 * A274280 A316265 A205477

Adjacent sequences: A132838 A132839 A132840 * A132842 A132843 A132844

Keyword

nonn

Author

Paul D. Hanna, Sep 12 2007

Status

approved