A270037 -id:A270037 - cp's OEIS frontend

A319033 a(n) is the (conjectured) largest number k that is zeroless in every base b such that n <= b < k.

7, 619, 26237, 698531, 3979433, 3979433, 29643151199, 29643151199, 29643151199, 29643151199, 260621258159, 260621258263, 260621258263, 296126238241, 296126238241, 296126238241, 296126238241, 556715917481, 971156053631, 971156053631, 971156053631, 971156053631

Offset: 2

Jon E. Schoenfield, Oct 08 2018

All terms are necessarily prime.
It seems nearly certain that there is no k > 7 that is zeroless in every base from 2 through k-1; if such a k exists, it exceeds 2^(10^9).
Up to 10^5000 (see A069575), no number k > 619 is zeroless in every base from 3 through k-1.
a(4) = 26237 or > 10^1000; a(5) = 698531 or > 10^1000; a(6) = a(7) = 3979433 unless a(7) > 10^1000; a(8) = a(9) = a(10) = a(11) = 29643151199 unless a(11) > 10^1000; it seems extremely unlikely that any of these terms could actually exceed 10^1000.

			a(2) = 7 because k = 7 = 111_2 = 21_3 = 13_4 = 12_5 = 11_6, with no zero digits in any base from 2 through k-1, and this is almost certainly (see Comments) the largest such number having this property.
a(3) = 619 because k = 619 = 211221_3 = 21223_4 = 4434_5 = 2511_6 = 1543_7 = 1153_8 = 757_9 = 619_10 = 513_11 = 437_12 = 388_13 = 323_14 = 2B4_15 = ... = 11_(k-1), and this is almost certainly (see Comments) the largest number having this property.

Cf. A052382, A069575, A270027, A270037, A277779.

cp's OEIS Frontend

A319033 a(n) is the (conjectured) largest number k that is zeroless in every base b such that n <= b < k.

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