A070152 Take pairs (x,y) with Sum_{j = x..y} j = concatenation of x and y. Sort pairs on y then x. This sequence gives x of each pair.

1, 2, 4, 13, 18, 33, 35, 7, 78, 133, 178, 228, 273, 388, 710, 1333, 1701, 1778, 2737, 3273, 3563, 3087, 3478, 12488, 13333, 14208, 17778, 31463, 36993, 5338, 7063, 9063, 12643, 15238, 17147, 22448, 23788, 27313, 29058, 34488, 36763, 38788, 43273, 50813, 53578

Offset

1,2

Comments

From Bernard Schott, Jan 26 2022: (Start)

Some subsequences, from Diophante and Crux Mathematicorum:

{(2*10^m-5)/15, m >= 1} = 1, 13, 133, 1333, ... = A097166.

{2*(4*10^m+5)/45, m >= 1} = 2, 18, 178, 1778, ...

{13*(26*100^m-125)/12375, m >= 2} = 273, 27313, 2731313, ... (End)

Links

Table of n, a(n) for n=1..45.

Diophante, A1945 - Concaténations en tous genres (in French).

R. Hoshino, Astonishing Pairs of Numbers, Crux Mathematicorum 27(1), 2001, p. 39-44.

Example

1+...+5 = 15; 2+...+7 = 27; 4+...+29 = 429; 13+...+53 = 1353; 18+...+63 = 1863.
133+...+533 = 133533.
273+...+2353 = 2732353.

Crossrefs

Cf. A070153, A071297, A186074.

Subsequence: A097166.

Sequence in context: A077319 A291901 A018701 * A176126 A240096 A018761

Adjacent sequences: A070149 A070150 A070151 * A070153 A070154 A070155

Keyword

nonn,base

Author

Lekraj Beedassy, May 06 2002

Extensions

More terms from David W. Wilson, Jun 04 2002

Name edited by Michel Marcus, Jan 29 2022

Status

approved