A390366 The total length of the base n sequence when starting from 2 and creating the smallest unused prime number, when read in base n, by either removing or changing or adding a single digit, from 0 to n-1, anywhere in the base n value of the previous number. If the base n sequence does not terminate, a(n) = -1.

11, 11, 862, 167, 679239, 178, 59061, 16928, 9656503, 917, 1217507499, 1001, 53029485, 4000129, 37671777, 27638

Offset

2,1

Comments

On removing the leading digit, any subsequent leading zeros are also removed.

Other known terms are a(13) = 1001, a(14) = 53029485, a(15) = 4000129, a(16) = 37671777, a(17) = 27638.

See A390367 for the last number in each base n sequence.

It is conjectured that the sequence of primes in base n terminates for all n.

Links

Table of n, a(n) for n=2..17.

Michael S. Branicky, Python program for OEIS A390366 and A390367

Example

a(2) = 11 as in base 2 the entire 11 term sequence is: 2 = 10_1, 3 = 11_1, 5 = 101_2, 7 = 111_2, 11 = 1011_2, 19 = 10011_2, 17 = 10001_2, 37 = 100101_2, 53 = 110101_2, 29 = 11101_2, 13 = 1101_2, and 13 is the final term as no prime that has not appeared can be created from removing, adding or changing a single digit to 0 or 1 from 1101_2.

Crossrefs

Cf. A390367 (last number), A389926, A387852, A372407.

Sequence in context: A268922 A328918 A362396 * A062129 A290298 A283218

Adjacent sequences: A390363 A390364 A390365 * A390367 A390368 A390369

Keyword

nonn,base,more

Author

Scott R. Shannon, Nov 03 2025

Extensions

a(12) from and a(13)-a(17) confirmed by Michael S. Branicky, Nov 06 2025

Status

approved