A370488 - OEIS

%I #27 Apr 12 2024 18:49:49

%S 1,3,11,13,57,65,95,99,124,132,159,165,246,265,335,342,353,397,406,

%T 422,426,482,876,1018,1383,1641,1689,1731,2376,2433,3149,3202,3294,

%U 3822,4068,4077,4192,4274,4554,4575,4712,5368,6283,6303,7997,8226,9815,10696,12273,12325,12764,12868

%N 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.

%H Nicolas Bělohoubek, <a href="/A370488/a370488_1.txt">Table of n, a(n) for n = 1..1000</a>

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

%o (PARI) avdev(v)={my(n=#v,sav=vecsum(v)/n);sum(k=1,n,abs(v[k]-sav))/n};

%o 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};

%o a370488(52) \\ _Hugo Pfoertner_, Feb 20 2024

%K nonn

%O 1,2

%A _Nicolas Bělohoubek_, Feb 19 2024