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%I #31 Oct 23 2022 01:34:17
%S 11,111,1111,11111,110011,111111,1100011,1111111,11000011,11100111,
%T 11111111,110000011,111000111,111111111,1100000011,1100110011,
%U 1110000111,1111001111,1111111111,11000000011,11001110011,11100000111,11110001111,11111111111,110000000011,110001100011
%N Digital representation of n contains only 1's and 0's, is palindromic and contains no singleton 1's or 0's.
%C The terms can be constructed by gluing together terms from A355280 with their reversal as follows: The terms with odd length L = 2k-1 are given from the k-digit terms of A355280 by replacing the last digit with the reversal of the term. (Equivalently, concatenate with the reversal and delete one of the middle digits.) Terms with an even number L = 2k of digits are given as concatenation(m, reverse(m)) = m*10^L(m) + A004086(m) where m runs over the k-digit terms from A355280, and the (k-1)-digit terms with the 1's complement of the last digit appended. This explains the formula given in CROSSREFS for the number of terms of given length. - _M. F. Hasler_, Oct 17 2022
%H Ray Chandler, <a href="/A061851/b061851.txt">Table of n, a(n) for n = 1..10000</a> (first 608 terms from N. J. A. Sloane)
%H N. J. A. Sloane, <a href="http://arxiv.org/abs/1307.0453">2178 And All That</a>, arXiv:1307.0453 [math.NT], 2013; Fib. Quart., 52 (2014), 99-120.
%F a(n) = A001232(n)/99 = A008918(n)/198.
%F a(n) = A007088(A222813(n)), where A007088 = write in binary. - _M. F. Hasler_, Oct 06 2022
%o (PARI) concat(apply( {A061851_row(n)=[fromdigits(binary(m))|m<-A222813_row(n)]}, [1..11])) \\ _M. F. Hasler_, Oct 17 2022
%o (Python)
%o def A061851_row(n): return [] if n < 2 else [10**n//9] if n < 6 else [
%o m*10**(n//2) + A004086(m//10) for m in A355280_row(n//2+1)] if n&1 else [
%o m*10**(n//2) + A004086(m) for m in sorted(A355280_row(n//2)+
%o [x*10+1-x%10 for x in A355280_row(n//2-1)])]
%o # _M. F. Hasler_, Oct 17 2022
%Y Number of terms with k digits is Fibonacci(floor(k/2)) = A000045(A004526(k)).
%Y Union of this sequence and twice this sequence is A061852 and 99 times that is A008919.
%Y Cf. A214927, A001232, A222814, A008918, A008919, A222813 (terms converted to decimal).
%Y Cf. A355280 (palindromic binary numbers with no digit run of length < 2).
%K base,nonn
%O 1,1
%A _Henry Bottomley_, May 10 2001
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