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

Author

Lekraj Beedassy, May 06 2002

Keywords

• nonn
• base

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)

Examples

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

Links

• Diophante, A1945 - Concaténations en tous genres (in French).
• R. Hoshino, Astonishing Pairs of Numbers, Crux Mathematicorum 27(1), 2001, p. 39-44.

Crossrefs

Cf. A070153, A071297, A186074.

Subsequence: A097166.

Extensions

More terms from David W. Wilson, Jun 04 2002

Name edited by Michel Marcus, Jan 29 2022