A068683 -id:A068683 - cp's OEIS frontend

A068685 Primes which are a sandwich of numbers using at most one digit between two 1's.

11, 101, 131, 151, 181, 191, 13331, 15551, 16661, 19991, 1333331, 1444441, 1777771, 188888881, 199999991, 1666666666661, 188888888888881, 16666666666666661, 1111111111111111111, 1666666666666666661, 155555555555555555551, 11111111111111111111111

Offset: 1

Amarnath Murthy, Mar 02 2002

a(47) has 1003 digits. - Michael S. Branicky, Jan 28 2023

			11 is a member sandwiching nothing between two 1's. 13331 is a sandwich using 333.

Michael S. Branicky, Table of n, a(n) for n = 1..46

Cf. A068683.

Select[Union[Flatten[Table[FromDigits[Join[{1},PadRight[{},n,i],{1}]], {n,0,20},{i,0,9}]]],PrimeQ] (* Harvey P. Dale, Mar 29 2012 *)

from sympy import isprime
from itertools import count, islice
def agen(): yield 11; yield from (t for i in count(1) for m in "0123456789" if isprime(t:=int("1" + m*i + "1")))
print(list(islice(agen(), 30))) # Michael S. Branicky, Jan 28 2023

More terms from Sascha Kurz, Mar 17 2002

a(21) and beyond from Michael S. Branicky, Jan 28 2023

A068684 Primes obtained as a concatenation p,q,p where p and q are successive primes and p

Original entry on oeis.org

353, 131713, 171917, 192319, 293129, 374137, 434743, 596159, 677167, 139149139, 163167163, 179181179, 223227223, 229233229, 269271269, 281283281, 347349347, 379383379, 547557547, 683691683, 761769761, 857859857, 863877863, 102110311021, 103910491039, 108710911087, 109110931091, 109310971093

Offset: 1

Amarnath Murthy, Mar 02 2002

			171917 is a prime which is the concatenation of 17, 19 and 17.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A068683, A078350.

cat3:= proc(a,b,c) local alpha,beta;
    beta:= ilog10(c)+1;
    alpha:= beta + ilog10(b)+1;
    10^alpha*a + 10^beta*b + c
end proc:
R:= NULL: count:= 0: q:= 2:
while count < 100 do
  p:= q; q:= nextprime(q);
  v:= cat3(p,q,p);
  if isprime(v) then R:= R,v; count:= count+1;
  fi
od:
R; # Robert Israel, Jul 01 2025

f(n)=prime(n)*(10^(ceil(log(prime(n+1))/log(10))+ceil(log(prime(n))/log(10))))+ prime(n+1)*10^ceil(log(prime(n))/log(10))+prime(n);
for(n=1,300, if(isprime(f(n))==1, print1(f(n),", ")))

More terms from Benoit Cloitre, Mar 21 2002

More terms from Robert Israel, Jul 02 2025

cp's OEIS Frontend

A068685 Primes which are a sandwich of numbers using at most one digit between two 1's.

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