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%I #36 May 25 2022 08:42:18
%S 0,0,1,0,2,0,3,0,4,0,1,4,5,0,6,0,7,0,8,0,1,8,9,0,2,8,10,0,3,8,11,0,12,
%T 0,1,12,13,0,14,0,15,0,16,0,1,16,17,0,2,16,18,0,3,16,19,0,4,16,20,0,1,
%U 4,5,16,17,20,21,0,6,16,22,0,7,16,23,0,24
%N Irregular table read by rows; the n-th row contains the sums of distinct terms of the n-th row of table A343835, in ascending order.
%C In other words, the n-th row contains the numbers k whose runs of 1's in the binary expansion also appear in that of n.
%C The n-th row has 2^A069010(n) terms.
%C This sequence has similarities with A295989.
%H Rémy Sigrist, <a href="/A343757/b343757.txt">Table of n, a(n) for n = 0..8120</a>
%H Rémy Sigrist, <a href="/A343757/a343757.png">Scatterplot of (n, T(n, k)) for n < 2^10</a>
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F T(n, 0) = 0.
%F T(n, 1) = A342410(n) for any n > 0.
%F T(n, 2^A069010(n)-1) = n.
%e Table begins:
%e 0: [0]
%e 1: [0, 1]
%e 2: [0, 2]
%e 3: [0, 3]
%e 4: [0, 4]
%e 5: [0, 1, 4, 5]
%e 6: [0, 6]
%e 7: [0, 7]
%e 8: [0, 8]
%e 9: [0, 1, 8, 9]
%e 10: [0, 2, 8, 10]
%e 11: [0, 3, 8, 11]
%e 12: [0, 12]
%e 13: [0, 1, 12, 13]
%e 14: [0, 14]
%e 15: [0, 15]
%e Table begins in binary:
%e 0: [0]
%e 1: [0, 1]
%e 10: [0, 10]
%e 11: [0, 11]
%e 100: [0, 100]
%e 101: [0, 1, 100, 101]
%e 110: [0, 110]
%e 111: [0, 111]
%e 1000: [0, 1000]
%e 1001: [0, 1, 1000, 1001]
%e 1010: [0, 10, 1000, 1010]
%e 1011: [0, 11, 1000, 1011]
%e 1100: [0, 1100]
%e 1101: [0, 1, 1100, 1101]
%e 1110: [0, 1110]
%e 1111: [0, 1111]
%o (PARI) row(n) = { my (rr=[]); while (n, my (z=valuation(n, 2), o=valuation(n/2^z+1, 2), r=(2^o-1)*2^z); n-=r; rr = concat(rr, r)); vector(2^#rr, k, vecsum(vecextract(rr, k-1))) }
%Y Cf. A069010, A295989, A343835.
%K nonn,base,tabf
%O 0,5
%A _Rémy Sigrist_, May 01 2021