A210625 Least semiprime dividing digit reversal of n, or 0 if no such factor.

0, 0, 0, 4, 0, 6, 0, 4, 9, 0, 0, 21, 0, 0, 51, 0, 0, 9, 91, 0, 4, 22, 4, 6, 4, 62, 4, 82, 4, 0, 0, 0, 33, 0, 0, 9, 0, 0, 93, 4, 14, 4, 34, 4, 6, 4, 74, 4, 94, 0, 15, 25, 35, 9, 55, 65, 15, 85, 95, 6, 4, 26, 4, 46, 4, 6, 4, 86, 4, 0, 0, 9, 0, 0, 57, 0, 77, 87

Offset: 1

Author

Jonathan Vos Post, Mar 24 2012

Keywords

• nonn
• base
• look
• easy

Comments

Roughly the analog of A209190 (least prime factor of reversal of digits), but with semiprimes (A001358) instead of primes (A000040).

Examples

			a(12) = min {k such that k|R(12) and k = p*q for primes p and q (not necessarily distinct)} = min {k, k|21 and k semiprime} = 21 = 3*7.
a(42) = min {k, k|24 and k semiprime} = min {4,6} = 4 = 2*2.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358, A004086, A004087, A011557, A209190, A210615.

Programs

Maple

r:= proc(n) option remember; local q;
      `if`(n<10, n, irem(n, 10, 'q') *10^(length(n)-1)+r(q))
    end:
a:= proc(n) local m, k;
      m:= r(n);
      for k from 4 to m do
         if irem(m, k)=0 and not isprime(k) and
            add(i[2], i=ifactors(k)[2])=2 then return k fi
      od; 0
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Mar 26 2012

Mathematica

spd[n_]:=Module[{sps=Select[Divisors[FromDigits[Reverse[ IntegerDigits[n]]]], PrimeOmega[#] == 2&,1]},If[sps=={},0,First[sps]]]; Array[spd,80] (* Harvey P. Dale, Aug 12 2012 *)

Formula

a(n) = A210615(R(n)) = A210615(A004086(n)).

a(p) = 0 iff p in (A004087 union A011557). - Alois P. Heinz, Mar 28 2012