A364972 Bases >= 2 in which the number of zeros needed to write the numbers 1 through k never equals k for any k.

3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 17, 18, 19, 20, 21, 22, 23, 25, 27, 30, 32, 35, 37, 38, 39, 40, 41, 43, 45, 48, 49, 53, 54, 57, 58, 59, 63, 65, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 79, 80, 83, 85, 88, 89, 90, 93, 94, 95, 96, 98, 100

Offset: 1

Author

Gregory Marton and Tanya Khovanova, Aug 14 2023

Keywords

• nonn
• more

Comments

We gave a theoretical upper bound, and experimentally checked values under that bound.

Examples

			11 and 13 are not in this sequence because exactly 3152738985031 zeros (expressed here for convenience in decimal) are needed to write the numbers from 1 to 3152738985031, and likewise 3950024143546664 for 13.
		

Links

• Tanya Khovanova and Gregory Marton, Archive Labeling Sequences, arXiv:2305.10357 [math.HO], 2023.
• Gregory Marton and Tanya Khovanova, Archive Labeling Sequences: Code (raw for text browsers) for supporting code and tables.

Crossrefs

Cf. A061217 (shows 10 is a term).