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A295079 a(n) = least k > n such that A002487(k) = A002487(n).

%I A295079 #13 Nov 15 2017 02:58:02
%S A295079 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 A295079 29,31,42,40,38,36,34,64,63,44,47,60,41,46,57,56,55,54,53,52,51,50,49,
%U A295079 96,61,58,90,62,71,84,59,80,78,65,67,72,70,68,66,128,76,126
%N A295079 a(n) = least k > n such that A002487(k) = A002487(n).
%C A295079 See A091926 for the least k such that A002487(k) = A002487(n).
%C A295079 For any n > 0, a(n) <= 2*n, with equality iff n belongs to A029744.
%C A295079 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 A295079 Rémy Sigrist, <a href="/A295079/b295079.txt">Table of n, a(n) for n = 1..8192</a>
%H A295079 <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>
%e A295079 A002487(n) = 5 for n = 11, 13, 17, 22, 26, 31, 34, 44, 52, 62, ...
%e A295079 Hence a(11) = 13, a(13) = 17, a(17) = 22, a(22) = 26, etc.
%o A295079 (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 A295079 a(n) = my (v=fusc(n)); for (k=n+1, oo, if (fusc(k)==v, return (k)))
%Y A295079 Cf. A000010, A002487, A029744, A091926.
%K A295079 nonn
%O A295079 1,1
%A A295079 _Rémy Sigrist_, Nov 13 2017