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

1,1

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.

Links

Table of n, a(n) for n=1..37.

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A004086, A034961.

Sequence in context: A247183 A321139 A096358 * A260349 A146147 A153758

Adjacent sequences: A359171 A359172 A359173 * A359175 A359176 A359177

Keyword

nonn,base

Author

Robert Israel, Dec 27 2022

Status

approved