A358427 a(n) is the least prime p such that there are exactly n primes q with the same number of digits as p such that the concatenations p|q and q|p are prime, or 0 if there is no such p.

2, 3, 13, 23, 19, 353, 157, 173, 101, 113, 137, 193, 181, 1831, 983, 1297, 2861, 1321, 1259, 1381, 1229, 1039, 1009, 1097, 1033, 1019, 1237, 1129, 1051, 1013, 1049, 1723, 1181, 1117, 1583, 1523, 1153, 1439

Offset

0,1

Comments

For every 5-digit prime p, there are at least 70 primes q. Thus it is very likely that a(n) = 0 for 38 <= n <= 69. However, there is no proof of this.

Links

Table of n, a(n) for n=0..37.

Example

a(4) = 19 because 19 is prime and there are 4 primes 13, 31, 79, 97 where 1913, 1319, 1931, 3119, 1979, 7931, 1397 and 9731 are prime, and no smaller prime works.

Maple

A:= Array(0..37): count:= 0: p:= 0:
while count < 38 do
  p:= nextprime(p);
  v:= f(p);
  if v <= 37 and A[v] = 0 then count:= count+1; A[v]:= p; fi;
od:
convert(A, list);

Prog

(Python)
from itertools import count, islice
from sympy import isprime, primerange
def agen(): # generator of terms
    adict, n = dict(), 0
    for d in count(1):
        pow = 10**d
        for p in primerange(10**(d-1), pow):
            v = 0
            for q in primerange(10**(d-1), pow):
                t = p*pow + q
                if isprime(p*pow + q) and isprime(q*pow + p): v += 1
            if v not in adict: adict[v] = p
            while n in adict: yield adict[n]; n += 1
print(list(islice(agen(), 38))) # Michael S. Branicky, Nov 15 2022

Crossrefs

Cf. A358421.

Sequence in context: A282342 A137248 A355438 * A136260 A296932 A288054

Adjacent sequences: A358424 A358425 A358426 * A358428 A358429 A358430

Keyword

nonn,base,more

Author

J. M. Bergot and Robert Israel, Nov 15 2022

Status

approved