A375243 Infinite variant of A375232.

0, 10, 20, 100, 30, 102, 40, 101, 203, 105, 60, 1024, 300, 107, 200, 150, 304, 1026, 80, 109, 230, 10457, 0, 120, 306, 110, 204, 1058, 303, 10279, 0, 1046, 302, 501, 0, 201, 3048, 170, 206, 1059, 330, 1042, 0, 1000, 320, 105678, 400, 210, 3000, 190, 202, 1045, 360, 1027, 800, 1001, 2034, 510, 0, 10269

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Aug 07 2024

Keywords

• nonn
• base

Comments

Instead of stopping the sequence when no integer is available, we extend it with 0 and go on (0 being the only term allowed to be repeated whenever nothing else works). This method seems to work ad infinitum.

Around 90% of the terms are not equal to 0.

For the first 1000 terms, the largest chunk between two successive 0 is the 24-integer long serie [101101, 2630, 8015, 40044, 10122, 333330, 1907, 200222, 10456, 10200, 80008, 101110, 3204, 5107, 6660, 9012, 1400, 202000, 8051, 10276, 40400, 101111, 20223, 5109].

Examples

			The finite sequence A375232 ends with 80, 109, 230, 10457. If we extend it with a(23) = 0, we can compute a(24) = 120, a(25) = 306 then 110, 204, 1058, 303 and 10279. No more integers are available at that stage. But, again, we can extend the sequence with a(31) = 0, then a(32) = 1046 and 302, 501, 0, 201, 3048, 170, etc.
A repeated single 0 is counted as a term of the sequence.
		

Crossrefs

Cf. A284516, A375232.