A032640 -id:A032640 - cp's OEIS frontend

A032650 Lucky numbers that are concatenations of a number k with itself.

33, 99, 2121, 2323, 5151, 5959, 6363, 7171, 7575, 8787, 8989, 9999, 105105, 111111, 117117, 123123, 129129, 135135, 143143, 147147, 153153, 171171, 173173, 177177, 191191, 201201, 237237, 243243, 255255, 263263, 285285, 305305, 309309, 317317

Offset: 1

Patrick De Geest, May 15 1998

Kevin P. Thompson, Table of n, a(n) for n = 1..4215 (first 95 terms from Amiram Eldar)

Intersection of A000959 and A020338.

Cf. A032640.

a(n) = A032640(n) || A032640(n), where || denotes concatenation. - Kevin P. Thompson, Nov 09 2021

More terms from Sascha Kurz, Mar 24 2002

Edited by Charles R Greathouse IV, Apr 26 2010

A032660 a(n) is the smallest positive k such that k concatenated with k + n is a lucky number.

Original entry on oeis.org

3, 6, 1, 2, 1, 4, 5, 6, 59, 2, 1, 4, 5, 6, 1, 6, 3, 2, 3, 10, 7, 2, 7, 4, 3, 4, 1, 14, 1, 2, 5, 10, 1, 2, 1, 2, 3, 6, 7, 2, 1, 14, 21, 10, 11, 6, 3, 4, 5, 6, 1, 12, 9, 34, 3, 22, 11, 2, 1, 2, 15, 18, 1, 12, 3, 2, 9, 6, 1, 12, 1, 2, 5, 4, 5, 8, 13, 8, 5, 4, 7, 2, 3, 2, 9, 4, 5, 2, 1, 8, 3, 4, 1, 6, 1

Offset: 0

Patrick De Geest, May 15 1998

First terms of sequences A032640-A032649, continued with displacements n > 9.

			77th term = 13: 13 + 76 (=77-1) = 89: '13' and '89' = 1389 equals a lucky number.

Michael De Vlieger, Table of n, a(n) for n = 0..1000

Cf. A000959, A032661.

Block[{L = Array[2 # + 1 &, 10^5 + 1, 0], m, n, r, s}, For[n = 2, n < Length[L], r = L[[n++]]; L = ReplacePart[L, Table[r*i -> Nothing, {i, 1, Length[L]/r}]]]; m = Max[L]; Array[Block[{k = 1}, While[And[# < m, FreeQ[L, #]] &@ Set[s, FromDigits@ Join[IntegerDigits[k], IntegerDigits[k + #]]], k++]; If[s <= m, k, -1]] &, 95, 0]] (* Michael De Vlieger, Jun 24 2020, after Jean-François Alcover at A000959 *)

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A032650 Lucky numbers that are concatenations of a number k with itself.

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A032660 a(n) is the smallest positive k such that k concatenated with k + n is a lucky number.

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