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 A102370 "Sloping binary numbers": write numbers in binary under each other (right-justified), read diagonals in upward direction, convert to decimal. 71
 0, 3, 6, 5, 4, 15, 10, 9, 8, 11, 14, 13, 28, 23, 18, 17, 16, 19, 22, 21, 20, 31, 26, 25, 24, 27, 30, 61, 44, 39, 34, 33, 32, 35, 38, 37, 36, 47, 42, 41, 40, 43, 46, 45, 60, 55, 50, 49, 48, 51, 54, 53, 52, 63, 58, 57, 56, 59, 126, 93, 76, 71, 66, 65, 64, 67, 70, 69 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS All terms are distinct, but certain terms (see A102371) are missing. But see A103122. Trajectory of 1 is 1, 3, 5, 15, 17, 19, 21, 31, 33, ..., see A103192. LINKS Seiichi Manyama, Table of n, a(n) for n = 0..10000 (first 1001 terms from T. D. Noe) David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers, J. Integer Seq. 8 (2005), no. 3, Article 05.3.6, 15 pp. Preprint versions: [pdf, ps]. Index entries for sequences related to binary expansion of n FORMULA a(n) = n + Sum_{ k >= 1 such that n + k == 0 mod 2^k } 2^k. (Cf. A103185.) In particular, a(n) >= n. - N. J. A. Sloane, Mar 18 2005 a(n) = A105027(A062289(n)) for n > 0. - Reinhard Zumkeller, Jul 21 2012 EXAMPLE ........0 ........1 .......10 .......11 ......100 ......101 ......110 ......111 .....1000 ......... The upward-sloping diagonals are: 0 11 110 101 100 1111 1010 ....... giving 0, 3, 6, 5, 4, 15, 10, ... The sequence has a natural decomposition into blocks (see the paper): 0; 3; 6, 5, 4; 15, 10, 9, 8, 11, 14, 13; 28, 23, 18, 17, 16, 19, 22, 21, 20, 31, 26, 25, 24, 27, 30; 61, ... Reading the array of binary numbers along diagonals with slope 1 gives this sequence, slope 2 gives A105085, slope 0 gives A001477 and slope -1 gives A105033. MAPLE A102370:=proc(n) local t1, l; t1:=n; for l from 1 to n do if n+l mod 2^l = 0 then t1:=t1+2^l; fi; od: t1; end; MATHEMATICA f[n_] := Block[{k = 1, s = 0, l = Max[2, Floor[Log[2, n + 1] + 2]]}, While[k < l, If[ Mod[n + k, 2^k] == 0, s = s + 2^k]; k++ ]; s]; Table[ f[n] + n, {n, 0, 71}] (* Robert G. Wilson v, Mar 21 2005 *) PROG (PARI) A102370(n)=n-1+sum(k=0, ceil(log(n+1)/log(2)), if((n+k)%2^k, 0, 2^k)) \\ Benoit Cloitre, Mar 20 2005 (PARI) {a(n) = if( n<1, 0, sum( k=0, length( binary( n)), bitand( n + k, 2^k)))} /* Michael Somos, Mar 26 2012 */ (Haskell) a102370 n = a102370_list !! n a102370_list = 0 : map (a105027 . toInteger) a062289_list -- Reinhard Zumkeller, Jul 21 2012 (Python) def a(n): return 0 if n<1 else sum([(n + k)&(2**k) for k in range(len(bin(n)[2:]) + 1)]) # Indranil Ghosh, May 03 2017 CROSSREFS Related sequences (1): A103542 (binary version), A102371 (complement), A103185, A103528, A103529, A103530, A103318, A034797, A103543, A103581, A103582, A103583. Related sequences (2): A103584, A103585, A103586, A103587, A103127, A103192 (trajectory of 1), A103122, A103588, A103589, A103202 (sorted), A103205 (base 10 version). Related sequences (3): A103747 (trajectory of 2), A103621, A103745, A103615, A103842, A103863, A104234, A104235, A103813, A105023, A105024, A105025, A105026, A105027, A105028. Related sequences (4): A105029, A105030, A105031, A105032, A105033, A105034, A105035, A105108. Related sequences (5): A105229, A105271, A104378, A104401, A104403, A104489, A104490, A104853, A104893, A104894, A105085. Sequence in context: A159067 A159058 A323778 * A291050 A268981 A353909 Adjacent sequences: A102367 A102368 A102369 * A102371 A102372 A102373 KEYWORD nonn,nice,easy,base,look AUTHOR Philippe Deléham, Feb 13 2005 EXTENSIONS More terms from Benoit Cloitre, Mar 20 2005 STATUS approved

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Last modified June 2 15:21 EDT 2023. Contains 363098 sequences. (Running on oeis4.)