A306747 Untouchable numbers with a record gap to the next untouchable number.

2, 5, 2642, 546046

Offset: 1

Author

Amiram Eldar, Mar 07 2019

Keywords

• nonn
• hard
• more

Comments

The record gap values are 3, 47, 62, 74.

Guy asks "How large can the gaps between untouchable numbers be?"

Examples

			5 is in the sequence since it is an untouchable number and the next untouchable number after it is 52 = 5 + 47 with a record gap of 47. The next gap which is larger than 47 occurs at 2642 which is followed by 2704 = 2642 + 62.
		

References

• Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section B10, p. 101.

Links

• Giovanni Resta, Untouchable numbers (terms up to 10^6)

Crossrefs

Cf. A005114, A231965.