A362535 Smallest prime ending with all base-n digits in consecutive order.

5, 59, 283, 3319, 95177, 6611219, 17119607, 1168314911, 100123456789, 3426593164037, 142731293952659, 304978405943587, 333425956286418337, 9635899740880849409, 535037563666793483759, 42192484763476168476011, 39482554816041508293677, 39574499346711396207137369

Offset

2,1

Comments

When written in base n, these are the smallest primes that end with the largest base-n metadrome (A023811).

a(386) has 1002 digits. - Michael S. Branicky, Apr 24 2023

Links

Michael S. Branicky, Table of n, a(n) for n = 2..385

Formula

a(n) = k*(n^n) + (-1 + n - n^2 + n^n)/((-1 + n)^2), where k > 0 is the least integer such that a(n) is prime.

Example

a(2) = 5 because 5 = 101_2.
a(3) = 59 because 59 = 2012_3.
a(4) = 283 because 283 = 10123_4.
a(12) = 16*(12^12) + (-1 + 12 - 12^2 + 12^12)/((-1+12)^2) = 142731293952659 is the least prime (at k = 16).

Maple

f:= proc(n) local k, s, m;
  s:= (-1 + n - n^2 + n^n)/((-1 + n)^2);
  m:= n^n;
  for k from 1 do if isprime(k*m+s) then return k*m+s fi od
end proc:
map(f, [$2..20]); # Robert Israel, Apr 28 2023

Prog

(Python)
from sympy import isprime
from itertools import count
def a(n):
    c, d = n**n, (-1 + n - n**2 + n**n)//((-1 + n)**2)
    return next(ak for ak in count(c+d, c) if isprime(ak))
print([a(n) for n in range(2, 23)]) # Michael S. Branicky, Apr 24 2023

Crossrefs

Cf. A023811.

Sequence in context: A179029 A049079 A024378 * A112461 A222585 A260630

Adjacent sequences: A362532 A362533 A362534 * A362536 A362537 A362538

Keyword

nonn,base

Author

Pedro A. B. A. Vinhas, Apr 24 2023

Extensions

a(17)-a(19) from Michael S. Branicky, Apr 24 2023

Status

approved