A390367 - OEIS

A390367

The final prime number in 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.

13, 53, 2557, 12239, 5888741, 653, 397459, 431329, 8074013, 5059, 3340970117, 5861, 531804751, 1036899713, 1415645447, 717427

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OFFSET

2,1

COMMENTS

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

Other known terms are a(13) = 5861, a(14) = 531804751, a(15) = 1036899713, a(16) = 1415645447, a(17) = 717427.

See A390366 for the total length of 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) = 13 as in base 2 the entire 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. A390366 (total length), A387852, A389926, A372407.

Sequence in context: A201486 A176617 A254895 * A358166 A372756 A195024

Adjacent sequences: A390364 A390365 A390366 * A390368 A390369 A390370

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