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 A206921 Rank of the n-th binary palindrome. The minimal number of iterations A206915(A206915(...A206915(A006995(n))...) such that the result is not a binary palindrome, a(3)=1. 2
 2, 1, 1, 1, 2, 1, 3, 1, 2, 1, 1, 1, 1, 1, 4, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The number of iterations such that A006995(n)=A006995(A006995(A006995(…(A206922(n)…) [For n<>3] . LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 FORMULA a(n)=k, where k can be determined by the following iteration: set k=0, p(0)=A006995(n). Repeat while A178225(p(k))==1, set k=k+1, p(k)=A206915(p(k-1)) end repeat [for n<>3]. Recursion for n<>3:   Case 1: a(n)=1, if n is not a binary palindrome;   Case 2: a(n)=a(A206915(n))+1, else. Formally: a(n)=if (A178225(n)==0) then 1 else a(A206915(n))+1 EXAMPLE a(1)=2, since A006995(1)=0=A006995(A006995(2)) [==> 2 iterations; 2 is not a binary palindrome]; a(3)=1 by definition; a(4)=1, since A006995(4)=5=A006995(4) [==> 1 iteration; 4 is not a binary palindrome]; a(7)=3, since A006995(7)=15=A006995(A006995(A006995(4))) [==> 3 iterations; 4 is not a binary palindrome]; PROG /* C program fragment, omitting formal details, n!=3 */ k=0; p=A006995(n); while A178225(p)==1 {   k++;   p=A206915(p); } return k; (PARI) up_to = 65537; A178225(n) = (Vecrev(n=binary(n))==n); A206915list(up_to) = { my(v=vector(up_to+1), s=0); for(n=1, up_to+1, s += A178225(n-1); v[n] = s); (v); }; v206915 = A206915list(up_to); A206915(n) = v206915[1+n]; A206921(n) = if((3==n)||!A178225(n), 1, 1+A206921(A206915(n))); \\ Antti Karttunen, Nov 14 2018 CROSSREFS Cf. A006995, A206922, A178225, A206915, A154809. Sequence in context: A211992 A182937 A185147 * A123529 A140747 A322373 Adjacent sequences:  A206918 A206919 A206920 * A206922 A206923 A206924 KEYWORD nonn,base AUTHOR Hieronymus Fischer, Mar 12 2012 STATUS approved

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Last modified April 24 22:26 EDT 2019. Contains 322446 sequences. (Running on oeis4.)