A334639 Lexicographically earliest infinite sequence of distinct positive integers such that the result of the division of a(n+1) by a(n) starts with the decimal number [a.b] with a = the rightmost digit of a(n), b = the leftmost digit of a(n+1) and the decimal point = the comma between a(n) and a(n+1).

2, 5, 26, 159, 1447, 10274, 45206, 280278, 2298281, 2757938, 22615092, 56537732, 118729239, 1080436075, 5942398413, 18421435081, 22105722098, 179056348994, 859470475172, 1804887997862, 4331731194869, 40718273231769, 378679941055453, 1173907817271905, 6573883776722668, 55878012102142678, 469375301657998496, 2910126870279590676, 17751773908705503124, 85208514761786414996

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, May 07 2020

Keywords

• base
• nonn

Comments

Some light backtracking is needed sometimes to let the sequence go to infinity (especially when a new integer ends in zero: we then increase it by 1).

Examples

			The sequence starts with 2, 5, 26, 159, 1447, 10274, 45206,...
a(2) = 5 divided by a(1) = 2 is 2.5;
a(3) = 26 divided by a(2) = 5 starts with 5.2;
a(4) = 159 divided by a(3) = 26 starts with 6.1;
a(5) = 1447 divided by a(4) = 159 starts with 9.1;
a(6) = 10274 divided by a(5) = 1447 starts with 7.1;
a(7) = 45206 divided by a(6) = 10274 starts with 4.4; etc.
		

References

• Eric Angelini, message to the Math-Fun mailing list on May 3rd 2020.

Links

• Jean-Marc Falcoz, Table of n, a(n) for n = 1..133

Crossrefs

Cf. A121805.