A235693 Semiprimes which have one or more occurrences of exactly five different digits.

10237, 10238, 10239, 10249, 10265, 10279, 10294, 10297, 10327, 10342, 10345, 10347, 10349, 10358, 10367, 10378, 10379, 10389, 10394, 10397, 10423, 10435, 10462, 10473, 10483, 10489, 10493, 10495, 10497, 10523, 10537, 10543, 10546, 10547, 10562, 10573, 10579

Offset: 1

Author

Colin Barker, Jan 14 2014

Keywords

• nonn
• base

Comments

The first term having a repeated digit is 100235.

The first term that is a square is 12769. - Robert Israel, Jul 06 2018

Links

• Robert Israel, Table of n, a(n) for n = 1..6240

Crossrefs

Cf. A235690-A235692, A235694-A235696.

Cf. A235154-A235161.

Programs

Maple

# to get all terms with 5 digits S:= combinat:-choose([$0..9],5):
f:= proc(x) local s,L;
      L:= convert(x,base,5);      if nops(L) < 5 then L:= [op(L),0$(5-nops(L))] fi;      if nops(convert(L,set))<5 then return NULL fi;
      op(select(t -> t > 10^4 and numtheory:-bigomega(t)=2, map(s -> add(s[L[i]+1]*10^(i-1),i=1..5),S)))
end proc:
sort(map(f, [$1..5^5-1])); # Robert Israel, Jul 06 2018

Mathematica

Select[Range[10000,11000],PrimeOmega[#]==2&&Count[DigitCount[#],0]==5&] (* Harvey P. Dale, Apr 08 2015 *)

PARI

list(lim)=my(v=List(), t); forprime(p=2, sqrt(lim), t=p; forprime(q=p, lim\t, listput(v, t*q))); vecsort(Vec(v)) \\ From A001358
b=list(15000); s=[]; for(n=1, #b, if(#vecsort(eval(Vec(Str(b[n]))),,8)==5, s=concat(s, b[n]))); s