A359174 First of three consecutive primes p, q, r, such that the reverse of p+q+r is divisible by at least one of p, q and r.

3, 7, 17, 53, 97, 193, 431, 1997, 5381, 30097, 128663, 278209, 385831, 481141, 1217509, 2401991, 2485831, 2625911, 3070037, 35912561, 39202231, 44531771, 45393841, 47084041, 50037011, 53639681, 54693481, 54949481, 55225217, 56094281, 56885351, 58632851, 59858651, 61030121, 62932621, 64195073, 64683491

Offset: 1

Author

Robert Israel, Dec 27 2022

Keywords

• nonn
• base

Comments

Suggested in an email from J. M. Bergot.

It appears that in most cases, p+q+r = 3*q and is a palindrome. This occurs for 109 of the 122 terms < 5*10^9.

Examples

			a(3) = 17 is a term because 17, 19, 23 are consecutive primes with 17 + 19 + 23 = 59 and the reverse of 59 is 95 which is divisible by 19.
		

Crossrefs

Cf. A004086, A034961.

Programs

Maple

rev:= proc(n) local L,i;
L:= convert(n,base,10);
add(L[-i]*10^(i-1),i=1..nops(L))
end proc:
q:= 2: r:= 3:
R:= NULL: count:= 0:
while count < 50 do
  p:= q; q:= r; r:= nextprime(r);
  x:= rev(p+q+r);
  if x mod p = 0 or x mod q = 0 or x mod r = 0 then count:= count+1; R:= R,p;
  fi;
od:
R;

Mathematica

q[tri_] := AnyTrue[tri, Divisible[IntegerReverse[Total[tri]], #] &]; Select[Partition[Prime[Range[250000]], 3, 1], q][[;; , 1]] (* Amiram Eldar, Dec 28 2022 *)

Python

from sympy import nextprime
from itertools import count, islice
def agen(): # generator of terms
    p, q, r = 2, 3, 5
    while True:
        t = int(str(p+q+r)[::-1])
        if any(t%s == 0 for s in (p, q, r)): yield p
        p, q, r = q, r, nextprime(r)
print(list(islice(agen(), 19))) # Michael S. Branicky, Dec 27 2022