A070152 - OEIS

%I #31 Jan 29 2022 12:15:56

%S 1,2,4,13,18,33,35,7,78,133,178,228,273,388,710,1333,1701,1778,2737,

%T 3273,3563,3087,3478,12488,13333,14208,17778,31463,36993,5338,7063,

%U 9063,12643,15238,17147,22448,23788,27313,29058,34488,36763,38788,43273,50813,53578

%N 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.

%C From _Bernard Schott_, Jan 26 2022: (Start)

%C Some subsequences, from Diophante and Crux Mathematicorum:

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

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

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

%H Diophante, <a href="http://www.diophante.fr/problemes-par-themes/arithmetique-et-algebre/a1-pot-pourri/1024-a1945-concatenations-en-tous-genres">A1945 - Concaténations en tous genres</a> (in French).

%H R. Hoshino, <a href="http://cms.math.ca/crux/v27/n1/public_page34-47.pdf">Astonishing Pairs of Numbers</a>, Crux Mathematicorum 27(1), 2001, p. 39-44.

%e 1+...+5 = 15; 2+...+7 = 27; 4+...+29 = 429; 13+...+53 = 1353; 18+...+63 = 1863.

%e 133+...+533 = 133533.

%e 273+...+2353 = 2732353.

%Y Cf. A070153, A071297, A186074.

%Y Subsequence: A097166.

%K nonn,base

%O 1,2

%A _Lekraj Beedassy_, May 06 2002

%E More terms from _David W. Wilson_, Jun 04 2002

%E Name edited by _Michel Marcus_, Jan 29 2022