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 A309776 Form a triangle: first row is n in base 2, next row is sums of pairs of adjacent digits of previous row, repeat until get a single number which is a(n). 1
 0, 1, 1, 2, 1, 2, 3, 4, 1, 2, 4, 5, 4, 5, 7, 8, 1, 2, 5, 6, 7, 8, 11, 12, 5, 6, 9, 10, 11, 12, 15, 16, 1, 2, 6, 7, 11, 12, 16, 17, 11, 12, 16, 17, 21, 22, 26, 27, 6, 7, 11, 12, 16, 17, 21, 22, 16, 17, 21, 22, 26, 27, 31, 32, 1, 2, 7, 8, 16, 17, 22, 23, 21, 22 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS a(n) = 1 occurs at n = 2^k for nonnegative integers k. LINKS Rémy Sigrist, Table of n, a(n) for n = 0..16384 FORMULA From Bernard Schott, Sep 22 2019: (Start) a(2^k + 1) = 2 for k >= 1 where 2^k+1 = 1000..0001_2. a(2^k - 1) = 2^(k-1) for k >= 2 where 2^k-1 = 111..111_2. a((4^k-1)/3) = 2^(2*k-3) for k >= 2 where (4^k-1)/3 = 10101..0101_2. (End) EXAMPLE For n=5 the triangle is   1 0 1    1 1     2 so a(5)=2. For n=14 we get   1 1 1 0    2 2 1     4 3      7 so a(14)=7. For n=26=11010_2; (n1+n2, n2+n3, n3+n4, n4+n5) = 2111; (n1'+n2', n2'+n3', n3'+n4') = 322; (n1''+n2'', n2''+n3'') = 54; (n1'''+n2''') = 9; a(26)= 9. PROG (PARI) a(n) = my (b=binary(n)); sum(k=1, #b, b[k]*binomial(#b-1, k-1)) \\ Rémy Sigrist, Aug 20 2019 CROSSREFS Cf. A306607. Sequence in context: A233782 A233972 A169778 * A255560 A328472 A046653 Adjacent sequences:  A309773 A309774 A309775 * A309777 A309778 A309779 KEYWORD nonn,base AUTHOR Cameron Musard, Aug 16 2019 EXTENSIONS Edited by N. J. A. Sloane, Sep 21 2019 Data corrected by Rémy Sigrist, Sep 22 2019 STATUS approved

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Last modified June 15 07:12 EDT 2021. Contains 345043 sequences. (Running on oeis4.)