A261645 -id:A261645 - cp's OEIS frontend

A261018 First differences of A260273.

2, 2, 3, 3, 4, 2, 3, 3, 4, 4, 2, 3, 3, 5, 7, 5, 5, 4, 3, 3, 5, 5, 3, 3, 4, 4, 4, 5, 7, 4, 5, 5, 4, 3, 3, 5, 5, 3, 3, 6, 8, 3, 3, 4, 4, 7, 4, 4, 5, 5, 5, 7, 7, 4, 5, 9, 5, 4, 4, 4, 3, 3, 3, 6, 3, 3, 6, 9, 5, 6, 5, 7, 8, 3, 3, 6, 3, 3, 4, 4, 4, 7, 4, 4, 8, 4, 4, 5, 5

Offset: 1

N. J. A. Sloane, Aug 17 2015

nonn

a(n) = A261461(A260273(n)). - Reinhard Zumkeller, Aug 30 2015

N. J. A. Sloane, Table of n, a(n) for n = 1..19999

Cf. A260273.

Cf. A261645, A261461.

a261018 n = a261018_list !! (n-1)
a261018_list = zipWith (-) (tail a260273_list) a260273_list
-- Reinhard Zumkeller, Aug 30 2015

b[1] = 1;
b[n_] := b[n] = Module[{bits, k}, bits = IntegerDigits[b[n-1], 2]; For[k = 1, True, k++, If[SequencePosition[bits, IntegerDigits[k, 2]] == {}, Return[b[n-1] + k]]]];
a[n_] := b[n+1] - b[n];
Array[a, 100] (* Jean-François Alcover, Aug 02 2018 *)

A261018_list, a = [], 1
for i in range(10**3):
    b, s = 1, format(a,'b')
    while format(b,'b') in s:
        b += 1
    a += b
    s = format(a,'b')
    A261018_list.append(b) # Chai Wah Wu, Aug 26 2015

A261644 Distance of A260273(n) to next power of 2.

Original entry on oeis.org

1, 1, 3, 8, 5, 1, 15, 12, 9, 5, 1, 31, 28, 25, 20, 13, 8, 3, 63, 60, 57, 52, 47, 44, 41, 37, 33, 29, 24, 17, 13, 8, 3, 127, 124, 121, 116, 111, 108, 105, 99, 91, 88, 85, 81, 77, 70, 66, 62, 57, 52, 47, 40, 33, 29, 24, 15, 10, 6, 2, 254, 251, 248, 245, 239

Offset: 1

Reinhard Zumkeller, Aug 30 2015

This sequence, as well as A261712, is suggested by A261396 and A261416.

			.  1: 1
.  2: 1
.  3: 3
.  4: 8,5,1
.  5: 15,12,9,5,1
.  6: 31,28,25,20,13,8,3
.  7: 63,60,57,52,47,44,41,37,33,29,24,17,13,8,3
.  8: 127,124,121,116,111,108,105,99,91,88,85,81,77,70,... (27 terms)
.  9: 254,251,248,245,239,236,233,227,218,213,207,202,195,,... (49 terms)

Reinhard Zumkeller, Rows n = 1..20 of triangle, flattened

Cf. A260273, A062383, A261645 (first differences), A261712 (reversed), A261646 (row lengths).

a261644 n = a261644_list !! (n-1)
a261644_list = zipWith (-)
               (map a062383 a260273_list) $ map fromIntegral a260273_list
a261644_tabf = [1] : f (tail $ zip a261645_list a261644_list) where
   f dxs = (map snd (dxs'' ++ [dx])) : f dxs' where
     (dxs'', dx:dxs') = span ((<= 0) . fst) dxs
a261644_row n = a261644_tabf !! (n-1)

a(n) = A062383(A260273(n)) - A260273(n).

A261789 First differences of A261786.

Original entry on oeis.org

2, 2, 3, 1, 2, 4, 3, 1, 3, 3, 3, 2, 2, 4, 2, 5, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 1, 4, 3, 2, 2, 4, 2, 4, 4, 4, 4, 2, 5, 5, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 4, 3, 3, 3, 3, 4, 3, 3, 1, 4, 3, 4, 4, 5, 3, 3, 3, 3, 3, 1, 4, 3, 4, 3, 3, 1, 4, 3, 2, 2, 4, 2, 4, 4

Offset: 1

Reinhard Zumkeller, Sep 01 2015

nonn

a(n) = A261787(A261786(n)).

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A261645, A261461, A261786, A261018, A261795.

a261789 n = a261789_list !! (n-1)
a261789_list = zipWith (-) (tail a261786_list') a261786_list'

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A261018 First differences of A260273.

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A261644 Distance of A260273(n) to next power of 2.

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A261789 First differences of A261786.

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