A389353 Primes p which are the concatenation of the last digits of the length(p) primes before and including p, where length(p) is the number of digits of p.

2, 3, 5, 7, 13, 71, 97, 397, 739, 99137, 139339, 1139917, 779919137, 97191997777319771, 3317719713399797917

Offset

1,1

Links

Table of n, a(n) for n=1..15.

Example

13 is a term since the last digits of 11 and 13 are 1, 3.
139339 is a term since the last digits of the 6 primes before and including it are: 1, 3, 9, 3, 3, 9.

Mathematica

pOK[p_]:=Module[{l=IntegerLength[p], s={IntegerDigits[p][[-1]]}}, Do[PrependTo[s, Last[IntegerDigits[NextPrime[p, -i]]]], {i, l-1}]; s==IntegerDigits[p]]; Select[Prime[Range[10^5]], pOK] (* James C. McMahon, Oct 14 2025 *)

Prog

(Python)
from sympy import isprime, prevprime
from itertools import count, islice, product
def ok(n):
    if not isprime(n): return False
    d, p = list(map(int, str(n))), prevprime(n)
    for i in range(2, len(d)+1):
        if p%10 != d[-i]: return False
        p = prevprime(p)
    return True
def agen(): # generator of terms
    yield from [2, 3, 5, 7]
    yield from (k for d in count(2) for t in product("1379", repeat=d) if ok(k:=int("".join(t))))
print(list(islice(agen(), 13))) # Michael S. Branicky, Oct 06 2025

Crossrefs

Cf. A055642, A091633.

Sequence in context: A055694 A249797 A346686 * A309249 A294727 A348352

Adjacent sequences: A389350 A389351 A389352 * A389354 A389355 A389356

Keyword

nonn,base,more

Author

Morné Louw, Oct 01 2025

Extensions

a(14) from Michael S. Branicky, Oct 06 2025

a(15) from Michael S. Branicky, Oct 13 2025

Status

approved