A370488 a(n) is the smallest integer k such that the average deviation of previous terms and k is an integer, where a(n) > a(n - 1) and a(1) = 1.

1, 3, 11, 13, 57, 65, 95, 99, 124, 132, 159, 165, 246, 265, 335, 342, 353, 397, 406, 422, 426, 482, 876, 1018, 1383, 1641, 1689, 1731, 2376, 2433, 3149, 3202, 3294, 3822, 4068, 4077, 4192, 4274, 4554, 4575, 4712, 5368, 6283, 6303, 7997, 8226, 9815, 10696, 12273, 12325, 12764, 12868

Offset: 1

Author

Nicolas Bělohoubek, Feb 19 2024

Keywords

• nonn

Links

• Nicolas Bělohoubek, Table of n, a(n) for n = 1..1000

Programs

PARI

avdev(v)={my(n=#v,sav=vecsum(v)/n);sum(k=1,n,abs(v[k]-sav))/n};
a370488(nterms) = {my(v=vector(nterms)); v[1]=1; for (k=2, nterms, for (j=v[k-1]+1, oo, v[k]=j; if (denominator(avdev(v[1..k])) == 1, break))); v};
a370488(52) \\ Hugo Pfoertner, Feb 20 2024

Formula

Conjecture: a(n)/n^3 tends to c, where 0.08 < c < 0.1.