A079058 Least k > 0 such that A025591(k) >= p(n) (p(n)=the n-th partition number).

1, 3, 5, 6, 7, 8, 9, 9, 10, 11, 11, 12, 12, 13, 13, 14, 14, 14, 15, 15, 16, 16, 16, 17, 17, 18, 18, 18, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 22, 22, 22, 22, 23, 23, 23, 24, 24, 24, 24, 25, 25, 25, 25, 26, 26, 26, 26, 27, 27, 27, 27, 28, 28, 28, 28, 28, 29, 29, 29, 29, 30, 30

Offset: 1

Author

Benoit Cloitre, Feb 02 2003

Keywords

• nonn

Crossrefs

Cf. A000041.

Programs

PARI

a(n)=if(n<0,0,k=1; while(polcoeff(prod(i=1,k,1+x^i),k*(k+1)\4)-polcoeff(1/eta(x),n)<0,k++); k)

Formula

a(n) is asymptotic to C*sqrt(n) with 3.5

Extensions

Name corrected by Sean A. Irvine, Jul 28 2025

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