A350781 Primes p whose reverse q is a semiprime, and of p+q and its reverse one is a prime and the other is a semiprime.

419, 599, 647, 12497, 13487, 14461, 15467, 15991, 16981, 17431, 17551, 18097, 18521, 18541, 19087, 19427, 20921, 20929, 22039, 22349, 22501, 22567, 22621, 22669, 22859, 24091, 24329, 24799, 26099, 26209, 26297, 26309, 26399, 26501, 26557, 26699, 26711, 26849, 28019, 28051, 28537, 28597, 28669

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3) = 647 is a term because 647 is prime, its reverse 746 = 2*373 is a semiprime, 647+746 = 1393 = 7*199 is a semiprime, and the reverse 3931 of 1393 is a prime.

Maple

filter:= proc(p) local q, r, s;
if not isprime(p) then return false fi;
q:= digrev(p);
if numtheory:-bigomega(q) <> 2 then return false fi;
r:= p+q;
s:= digrev(r);
{numtheory:-bigomega(r), numtheory:-bigomega(s)} = {1, 2}
end proc:
digrev:= proc(n) local L, i;
L:= convert(n, base, 10);
add(L[-i]*10^(i-1), i=1..nops(L))
end proc:
select(filter, [seq(i, i=3..10^5, 2)]);

Mathematica

semiQ[n_] := PrimeOmega[n] == 2; q1[p_] := PrimeQ[p] && semiQ[IntegerReverse[p]]; q2[p_] := semiQ[p] && PrimeQ[IntegerReverse[p]]; q[p_] := q1[p] && (q1[(s = p + IntegerReverse[p])] || q2[s]); Select[Range[30000], q] (* Amiram Eldar, Jan 16 2022 *)

Prog

(Python)
from sympy import isprime, factorint
def issemip(n): return sum(factorint(n).values()) == 2
def ok(p):
    if not isprime(p): return False
    q = int(str(p)[::-1])
    if not issemip(q): return False
    r = int(str(p+q)[::-1])
    return (isprime(p+q) and issemip(r)) or (isprime(r) and issemip(p+q))
print([k for k in range(30000) if ok(k)]) # Michael S. Branicky, Jan 15 2022

Crossrefs

Cf. A001358.

Subsequence of A085778.

Sequence in context: A292422 A328497 A138062 * A097233 A233551 A142281

Adjacent sequences: A350778 A350779 A350780 * A350782 A350783 A350784

Keyword

nonn,base

Author

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

Status

approved