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 A343835 Irregular table T(n, k), n > 0, k = 1..A069010(n), read by rows; the n-th row contains the shortest partition of n whose values belong to A023758 and can be added without carriers in binary, in descending order. 3
 1, 2, 3, 4, 4, 1, 6, 7, 8, 8, 1, 8, 2, 8, 3, 12, 12, 1, 14, 15, 16, 16, 1, 16, 2, 16, 3, 16, 4, 16, 4, 1, 16, 6, 16, 7, 24, 24, 1, 24, 2, 24, 3, 28, 28, 1, 30, 31, 32, 32, 1, 32, 2, 32, 3, 32, 4, 32, 4, 1, 32, 6, 32, 7, 32, 8, 32, 8, 1, 32, 8, 2, 32, 8, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS In other words, the n-th row gives the numerical values of the runs of 1's in the binary expansion of n. LINKS Rémy Sigrist, Table of n, a(n) for n = 1..6145 Index entries for sequences related to binary expansion of n FORMULA T(n, 1) = A342126(n). T(n, A069010(n)) = A342410(n). Sum_{k = 1..A069010(n)} T(n, k) = n. EXAMPLE Table begins: 1: [1] 2: [2] 3: [3] 4: [4] 5: [4, 1] 6: [6] 7: [7] 8: [8] 9: [8, 1] 10: [8, 2] 11: [8, 3] 12: [12] 13: [12, 1] 14: [14] 15: [15] Table begins in binary: 1: [1] 10: [10] 11: [11] 100: [100] 101: [100, 1] 110: [110] 111: [111] 1000: [1000] 1001: [1000, 1] 1010: [1000, 10] 1011: [1000, 11] 1100: [1100] 1101: [1100, 1] 1110: [1110] 1111: [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(r, rr); ); rr } CROSSREFS Cf. A023758, A069010, A272011, A342126, A342410, A343757. Sequence in context: A346617 A160386 A347860 * A307310 A339072 A174015 Adjacent sequences: A343832 A343833 A343834 * A343836 A343837 A343838 KEYWORD nonn,base,tabf,easy AUTHOR Rémy Sigrist, May 01 2021 STATUS approved

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Last modified June 17 06:41 EDT 2024. Contains 373432 sequences. (Running on oeis4.)