A358420 Primes that are the concatenation p|q of two primes p and q with the same number of digits, where r = (p+q)/2, r|q and p|r are all primes.

1123, 101197, 101293, 101797, 107827, 109313, 113149, 151163, 151607, 151643, 163199, 163811, 179947, 193541, 211271, 223331, 239263, 251263, 251443, 263191, 271967, 281353, 281557, 307367, 331283, 337397, 353929, 359167, 359599, 367547, 383659, 383983, 389569, 401773, 419467, 421241, 421397

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Example

a(3) = 101293 is a term because 101293, 101, 293, (101+293)/2 = 197, 101197 and 197293 are all primes.

Maple

Res:= NULL: count:= 0:
for d from 2 by 2 while count < 100 do
  pq:= 10^(d-1);
  while count < 100 do
    pq:= nextprime(pq);
    if pq > 10^d then break fi;
    q:= pq mod 10^(d/2);
    if q < 10^(d/2-1) then next fi;
    p:= (pq-q)/10^(d/2);
    r:= (p+q)/2;
    if not (r::integer and isprime(q) and isprime(p) and isprime(r)) then next fi;
    if isprime(p*10^(d/2)+r) and isprime(r*10^(d/2)+q) then Res:= Res, pq; count:= count+1; fi
  od;
od:
Res;

Prog

(Python)
from itertools import count, islice
from sympy import isprime, primerange
def agen(): # generator of terms
    for d in count(1):
        pow = 10**d
        for p in primerange(10**(d-1), pow):
            for q in primerange(10**(d-1), pow):
                t = p*pow + q
                if isprime(t):
                    r = (p+q)//2
                    if all(isprime(t) for t in [r, r*pow + q, p*pow + r]):
                        yield t
print(list(islice(agen(), 37))) # Michael S. Branicky, Nov 15 2022

Crossrefs

Contained in A358421.

Sequence in context: A261264 A125840 A069984 * A104285 A260898 A358395

Adjacent sequences: A358417 A358418 A358419 * A358421 A358422 A358423

Keyword

nonn,base

Author

J. M. Bergot and Robert Israel, Nov 14 2022

Status

approved