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 A343757 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. 2
 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, 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, 4, 5, 16, 17, 20, 21, 0, 6, 16, 22, 0, 7, 16, 23, 0, 24 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS 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. The n-th row has 2^A069010(n) terms. This sequence has similarities with A295989. LINKS Rémy Sigrist, Table of n, a(n) for n = 0..8120 Rémy Sigrist, Scatterplot of (n, T(n, k)) for n < 2^10 FORMULA T(n, 0) = 0. T(n, 1) = A342410(n) for any n > 0. T(n, 2^A069010(n)-1) = n. EXAMPLE Table begins: 0: [0] 1: [0, 1] 2: [0, 2] 3: [0, 3] 4: [0, 4] 5: [0, 1, 4, 5] 6: [0, 6] 7: [0, 7] 8: [0, 8] 9: [0, 1, 8, 9] 10: [0, 2, 8, 10] 11: [0, 3, 8, 11] 12: [0, 12] 13: [0, 1, 12, 13] 14: [0, 14] 15: [0, 15] Table begins in binary: 0: [0] 1: [0, 1] 10: [0, 10] 11: [0, 11] 100: [0, 100] 101: [0, 1, 100, 101] 110: [0, 110] 111: [0, 111] 1000: [0, 1000] 1001: [0, 1, 1000, 1001] 1010: [0, 10, 1000, 1010] 1011: [0, 11, 1000, 1011] 1100: [0, 1100] 1101: [0, 1, 1100, 1101] 1110: [0, 1110] 1111: [0, 1111] PROG (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))) } CROSSREFS Cf. A069010, A295989, A343835. Sequence in context: A108416 A215395 A338569 * A108760 A343554 A137304 Adjacent sequences: A343754 A343755 A343756 * A343758 A343759 A343760 KEYWORD nonn,base,tabf AUTHOR Rémy Sigrist, May 01 2021 STATUS approved

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Last modified January 29 23:01 EST 2023. Contains 359939 sequences. (Running on oeis4.)