A295079 - OEIS

%I #13 Nov 15 2017 02:58:02

%S 2,4,6,8,7,12,10,16,15,14,13,24,17,20,18,32,22,30,23,28,27,26,25,48,

%T 29,31,42,40,38,36,34,64,63,44,47,60,41,46,57,56,55,54,53,52,51,50,49,

%U 96,61,58,90,62,71,84,59,80,78,65,67,72,70,68,66,128,76,126

%N a(n) = least k > n such that A002487(k) = A002487(n).

%C See A091926 for the least k such that A002487(k) = A002487(n).

%C For any n > 0, a(n) <= 2*n, with equality iff n belongs to A029744.

%C For any n > 0, there is a constant i >= 0 such that for any k >= 0, a^(i + k*A000010(A002487(n)))(n) = 2^k * a^i(n) (where a^m denotes the m-th iterate of the sequence a); this comes from the fact that a value v > 0 eventually appears A000010(v) times in each row of A002487.

%H Rémy Sigrist, <a href="/A295079/b295079.txt">Table of n, a(n) for n = 1..8192</a>

%H <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>

%e A002487(n) = 5 for n = 11, 13, 17, 22, 26, 31, 34, 44, 52, 62, ...

%e Hence a(11) = 13, a(13) = 17, a(17) = 22, a(22) = 26, etc.

%o (PARI) fusc(n)=local(a=1, b=0); while(n>0, if(bitand(n, 1), b+=a, a+=b);n>>=1); b \\ after _Charles R Greathouse IV_ at A002487

%o a(n) = my (v=fusc(n)); for (k=n+1, oo, if (fusc(k)==v, return (k)))

%Y Cf. A000010, A002487, A029744, A091926.

%K nonn

%O 1,1

%A _Rémy Sigrist_, Nov 13 2017