A090540 Beginning with 3, least prime obtained by sandwiching the previous term between strings of identical digits.

3, 131, 11311, 771131177, 33337711311773333, 77777733337711311773333777777, 3777777333377113117733337777773, 33377777733337711311773333777777333, 333333337777773333771131177333377777733333333, 9933333333777777333377113117733337777773333333399, 33333993333333377777733337711311773333777777333333339933333

Offset

1,1

Comments

Questions: (1) Is this sequence infinite? (2) If so, are the digits equally distributed? - Stefan Steinerberger, Nov 08 2005

a(21) has 1051 digits. - Michael S. Branicky, Jun 13 2026

Links

Michael S. Branicky, Table of n, a(n) for n = 1..20

Prog

(Python)
from itertools import count, islice
from sympy import isprime
def agen(): # generator of terms
    an = 3
    while True:
        yield an
        s = str(an)
        an = next(t for k in count(1) for sk in [d*k for d in "1379"] if isprime(t:=int(sk + s + sk)))
print(list(islice(agen(), 11))) # Michael S. Branicky, Jun 13 2026

Crossrefs

Sequence in context: A262639 A082563 A083999 * A262643 A048796 A213203

Adjacent sequences: A090537 A090538 A090539 * A090541 A090542 A090543

Keyword

base,nonn

Author

Amarnath Murthy, Dec 09 2003

Extensions

a(6)-a(8) from Jim Nastos, Jan 30 2004

a(9)-a(11) from Stefan Steinerberger, Nov 08 2005

Status

approved