A053583 a(n+1) is the smallest prime ending with (but not equal to) a(n), where a(1)=3.

3, 13, 113, 2113, 12113, 612113, 11612113, 1611612113, 111611612113, 1111611612113, 81111611612113, 2181111611612113, 132181111611612113, 11132181111611612113, 3411132181111611612113, 413411132181111611612113, 12413411132181111611612113

Offset: 1

Author

G. L. Honaker, Jr., Jan 18 2000

Keywords

• base
• nonn

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..370 (terms 1..210 from Robert Israel)

Crossrefs

Cf. A000040, A053582, A053584, A069612.

Programs

Maple

A[1]:= 3;
for n from 2 to 100 do
d:= 10^(ilog10(A[n-1])+1);
for k from 1 do
  p:= A[n-1]+d*k;
  if isprime(p) then
    A[n]:= p;
    break
  fi
od
od:
seq(A[n],n=1..100); # Robert Israel, Jul 15 2014

Python

from sympy import isprime
from itertools import count, islice
def agen(an=3):
    while True:
        yield an
        pow10 = 10**len(str(an))
        for t in count(pow10+an, step=pow10):
            if isprime(t):
                an = t
                break
print(list(islice(agen(), 17))) # Michael S. Branicky, Jun 23 2022

Extensions

Definition corrected by Robert Israel, Jul 15 2014