A182150 Semiprimes that are also semiprime when their digits are sorted into nondecreasing order.

4, 6, 9, 14, 15, 22, 25, 26, 33, 34, 35, 38, 39, 46, 49, 51, 55, 57, 58, 62, 69, 77, 85, 93, 94, 111, 115, 118, 119, 122, 123, 129, 133, 134, 143, 145, 146, 155, 158, 159, 166, 169, 177, 178, 185, 187, 202, 205, 206, 213, 219, 221, 226, 235, 237, 247, 249, 253

Offset: 1

Author

Jonathan Vos Post, Apr 18 2012

Keywords

• nonn
• base
• easy

Comments

This is to A211654 primes that are also prime when their digits are sorted into nondecreasing order as A001358 semiprimes are to A000040 primes. There is an ambiguity arising from OEIS conventions, exemplified by the semiprime 303, which sorts to 033 and truncates to the semiprime 33.

Examples

			51 is in the sequence because, though it is a semiprime whose digits are in descending order, once the digits are sorted to be nondecreasing, it is the semiprime 15, whose digits are (left to right) nondecreasing.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001358, A097393, A211654.

Programs

Maple

h:= proc(m) local k; for k from m+1 while isprime(k) or
            add(i[2], i=ifactors(k)[2])<>2 do od; k
    end:
a:= proc(n) option remember; local k, l, s;
      k:= h(a(n-1));
      do l:= sort(convert(k, base, 10));
         s:= add(l[i]*10^(nops(l)-i), i=1..nops(l));
         if h(s-1)=s then return k else k:=h(k) fi
      od
    end: a(0):=0:
seq(a(n), n=1..100);  # Alois P. Heinz, Apr 22 2012

Mathematica

Select[Range[300],PrimeOmega[#]==2&&PrimeOmega[FromDigits[ Sort[ IntegerDigits[ #]]]]==2&] (* Harvey P. Dale, Nov 13 2014 *)

Extensions

More terms from Alois P. Heinz, Apr 22 2012