A239092 -id:A239092 - cp's OEIS frontend

A076489 Number of common (distinct) digits of consecutive natural numbers.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 2

Offset: 0

Labos Elemer, Oct 21 2002

a(A226637(n)) = 0. Reinhard Zumkeller, Sep 01 2013

This is the prefix overlap between the decimal expansions of n and n+1 (cf. A238845). - N. J. A. Sloane, Mar 22 2014

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Cf. A001477, A031298, A076490, A238845, A239092 (partial sums).

import Data.List (intersect, nub)
a076489 n = a076489_list !! n
a076489_list = map (length . nub) $
               zipWith intersect (tail a031298_tabf) a031298_tabf
-- Reinhard Zumkeller, Sep 01 2013

Table[Length[Intersection[IntegerDigits[w], IntegerDigits[w+1]]], {w, 0, 200}]

Initial zero prepended and offset adjusted by Reinhard Zumkeller, Sep 01 2013

A239091 Prefix overlap of dictionary consisting of binary expansions of 0 through n.

Original entry on oeis.org

0, 1, 2, 3, 5, 6, 8, 9, 12, 14, 17, 18, 21, 23, 26, 27, 31, 34, 38, 40, 44, 47, 51, 52, 56, 59, 63, 65, 69, 72, 76, 77, 82, 86, 91, 94, 99, 103, 108, 110, 115, 119, 124, 127, 132, 136, 141, 142, 147, 151, 156, 159, 164, 168, 173, 175, 180, 184, 189, 192, 197, 201, 206

Offset: 1

N. J. A. Sloane, Mar 22 2014

The prefix overlap of a dictionary is the sum of the prefix overlaps between successive words.

Partial sums of A238845.

			For n=5 the dictionary is
0
1
10
11
100
101
and the successive prefix overlaps are 0,1,1,1,2, whose sum is a(5)=5.

Alois P. Heinz, Table of n, a(n) for n = 1..10000
Rodica Simion and Herbert S. Wilf, The distribution of prefix overlap in consecutive dictionary entries, SIAM J. Algebraic Discrete Methods, 7(1986), no. 3, 470--475. MR0844051.

Cf. A000523, A011371, A061168, A238845, A239092.

a(n) = A061168(n+1) - A011371(n+1) + A000523(n+1). - Alan Michael Gómez Calderón, Jul 17 2025

cp's OEIS Frontend

A076489 Number of common (distinct) digits of consecutive natural numbers.

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