A068687 -id:A068687 - cp's OEIS frontend

A068689 Primes which are a sandwich of numbers made of only one decimal digit between two 9's.

919, 929, 9222229, 9888889, 9222222222229, 9888888888888888888888888888888888888888888888888888888888888888888888889

Offset: 1

Amarnath Murthy, Mar 02 2002

Conjecture: Inner digits 1, 2 and 8 are the only repeating digits for which the resulting numbers can be prime for outer digits 9. I.e., 9444..4449, 9555..5559, 9777..7779 are composite. The cases for inner digits 0, 3, 6 and 9 give composite numbers. - Cino Hilliard, Jul 11 2005

a(13) has 1141 digits. - Michael S. Branicky, Jan 28 2023

Michel Marcus, Table of n, a(n) for n = 1..12

Cf. A068685, A068687, A068688.

lista(nn) = my(list = List(), p); for (n=1, nn, for (k=1, 8, my(d=vector(n, i, k)); d = concat(9, d); d = concat(d, 9); if (ispseudoprime(p=fromdigits(d)), listput(list, p)););); Vec(list); \\ Michel Marcus, Jan 28 2023

from sympy import isprime
from itertools import count, islice
def agen(): yield from (t for i in count(1) for m in "124578" if isprime(t:=int("9" + m*i + "9")))
print(list(islice(agen(), 11))) # Michael S. Branicky, Jan 28 2023

More terms from Sascha Kurz, Mar 17 2002

A068688 Primes which are a sandwich of numbers made of only one digit between two 7's.

Original entry on oeis.org

727, 757, 787, 797, 72227, 75557, 76667, 78887, 79997, 7666667, 722222227, 74444444447, 75555555557, 755555555555555555557, 75555555555555555555557, 72222222222222222222222222227, 79999999999999999999999999997, 7444444444444444444444444444447

Offset: 1

Amarnath Murthy, Mar 02 2002

The middle digit is never 0, 1, 3, or 7. - Harvey P. Dale, May 05 2018

a(40) has 1213 digits. - Michael S. Branicky, Jan 28 2023

Harvey P. Dale, Table of n, a(n) for n = 1..39

Cf. A068685, A068687, A068689.

Select[Flatten[Table[10FromDigits[PadRight[{7},n,i]]+7,{n,2,100},{i,9}]],PrimeQ] (* Harvey P. Dale, May 05 2018 *)

from sympy import isprime
from itertools import count, islice
def agen(): yield from (t for i in count(1) for m in "0123456789" if isprime(t:=int("7" + m*i + "7")))
print(list(islice(agen(), 30))) # Michael S. Branicky, Jan 28 2023

More terms from Sascha Kurz, Mar 17 2002

cp's OEIS Frontend

A068689 Primes which are a sandwich of numbers made of only one decimal digit between two 9's.

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