A097393 Emirpimes: numbers n such that n and its reversal are distinct semiprimes.

15, 26, 39, 49, 51, 58, 62, 85, 93, 94, 115, 122, 123, 129, 143, 155, 158, 159, 169, 177, 178, 183, 185, 187, 203, 205, 221, 226, 265, 289, 302, 314, 319, 321, 326, 327, 329, 335, 339, 341, 355, 381, 394, 398, 413, 415, 437, 493, 497, 502, 511, 514, 533

Offset

1,1

Comments

Computed by Eric W. Weisstein, Aug 13 2004.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Emirpimes

Example

26 is a semiprime, as it is 2 * 13, and so is 62 = 2 * 31. 26 and 62 are therefore both in the sequence.

Maple

isA097393 := proc(n)
    local R ;
    R := digrev(n) ;
    if R <> n then
        if numtheory[bigomega](R) = 2 and numtheory[bigomega](n) = 2 then
            return true;
        else
            false;
        end if;
      else
        false;
    end if;
end proc:
for n from 1 to 500 do
    if isA097393(n) then
        printf("%d, ", n) ;
    end if;
end do: # R. J. Mathar, Apr 05 2012

Mathematica

Cases[{#, IntegerReverse@#} & /@ DeleteCases[Range@5000, _?PalindromeQ], {_?(PrimeOmega@# == 2 &) ..}][[All, 1]] (* Hans Rudolf Widmer, Jan 07 2024 *)

Prog

(PARI) rev(n)=subst(Polrev(digits(n)), 'x, 10)
issemi(n)=bigomega(n)==2
list(lim)=my(v=List(), r); forprime(p=2, lim\2, forprime(q=2, min(lim\p, p), r=rev(p*q); if(issemi(r)&&r!=p*q, listput(v, p*q)))); Set(v) \\ Charles R Greathouse IV, Jan 27 2015
(Python)
from sympy import factorint
from itertools import islice
def sp(n): f = factorint(n); return sum(f[p] for p in f) == 2
def ok(n): r = int(str(n)[::-1]); return r != n and sp(n) and sp(r)
print([k for k in range(534) if ok(k)]) # Michael S. Branicky, Jul 03 2022

Crossrefs

Cf. A001358, A097394.

Equals A085751 \ A046328.

Sequence in context: A366961 A032609 A050699 * A050700 A373731 A263108

Adjacent sequences: A097390 A097391 A097392 * A097394 A097395 A097396

Keyword

nonn,base

Author

Jonathan Vos Post

Status

approved