A233419 - OEIS

%I #11 Dec 10 2013 02:39:55

%S 1,2,6,7,12,3,21,14,15,4,5,72,73,42,34,6,29,18,7,8,21,23,144,9,273,

%T 146,97,10,68,30,11,12,76,102,36,130,13,14,90,67,42,15,72,45,75,16,17,

%U 1056,1057,546,185,18,194,54,19,20,95,97,60,495,21,22,105,107,152,23,112

%N Least m such that A232637(m) is divisible by k, where k is the n-th number not divisible by 4; or 0 if no such m exists.

%C Conjecture: a(n) > 0 for all n. Equivalently, any number not divisible by 4 divides infinitely many members of A232637.

%H Charles R Greathouse IV, <a href="/A233419/b233419.txt">Table of n, a(n) for n = 1..10000</a>

%o (PARI) ok(n)=hammingweight(n)%2 && hammingweight(n\2+1)%2

%o a(n)=my(k=n+(n-1)\3,m=k);while(!ok(m), m+=k); (m+6)\4 \\ _Charles R Greathouse IV_, Dec 09 2013

%Y Cf. A232637, A000069, A042968.

%K nonn

%O 1,2

%A _Charles R Greathouse IV_, Dec 09 2013