A349709 Primes p such that if q is the next prime, A004086(p*q) = A004086(p)*A004086(q).

2, 7, 11, 97, 101, 1021, 1201, 2003, 3001, 10103, 10111, 20011, 20021, 21001, 101111, 102001, 102101, 112103, 112111, 120103, 201011, 202001, 1000003, 1000211, 1010003, 1010201, 1011001, 1020011, 1100101, 1100311, 1111013, 1111021, 1112003, 1201001, 2011201, 2020001, 2100001, 2100011, 10000103

Offset: 1

Author

J. M. Bergot and Robert Israel, Jan 05 2022

Keywords

• nonn
• base

Examples

			a(6) = 1021 is a term because it is prime, the next prime is 1031, and the reverse of 1021*1031 = 1052651 is 1562501 = 1301*1201.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..169

Crossrefs

Cf. A004086.

Programs

Maple

revdigs:= proc(n) local L,i,m;
  L:= convert(n,base,10);
  m:= nops(L);
  add(L[i]*10^(m-i),i=1..m)
end proc:
R:= NULL: count:= 0:
q:= 2: qr:= 2:
while count < 50 do
  p:= q; pr:= qr;
  q:= nextprime(q); qr:= revdigs(q);
  if pr*qr = revdigs(p*q) then
     count:= count+1; R:= R, p;
  fi
od:
R;

Mathematica

seqQ[p_] := PrimeQ[p] && Module[{r = IntegerReverse, q = NextPrime[p]}, r[p*q] == r[p] * r[q]]; Select[Range[2.2*10^6], seqQ] (* Amiram Eldar, Jan 05 2022 *)

PARI

R(n) = fromdigits(Vecrev(digits(n))); \\ A004086
isok(p) = if (isprime(p), my(q=nextprime(p+1)); R(p*q) == R(p)*R(q)); \\ Michel Marcus, Jan 05 2022

Python

from itertools import islice
from sympy import isprime, nextprime
def R(n): return int(str(n)[::-1])
def agen(): # generator of terms
    p, pr = 2, 2
    while True:
        q = nextprime(p)
        qr = R(q)
        if R(p*q) == pr * qr:
            yield p
        p, pr = q, qr
print(list(islice(agen(), 38))) # Michael S. Branicky, Jan 05 2022