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A235693 Semiprimes which have one or more occurrences of exactly five different digits. 3

%I #18 Jul 06 2018 23:15:34

%S 10237,10238,10239,10249,10265,10279,10294,10297,10327,10342,10345,

%T 10347,10349,10358,10367,10378,10379,10389,10394,10397,10423,10435,

%U 10462,10473,10483,10489,10493,10495,10497,10523,10537,10543,10546,10547,10562,10573,10579

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

%C The first term having a repeated digit is 100235.

%C The first term that is a square is 12769. - _Robert Israel_, Jul 06 2018

%H Robert Israel, <a href="/A235693/b235693.txt">Table of n, a(n) for n = 1..6240</a>

%p # to get all terms with 5 digits S:= combinat:-choose([$0..9],5):

%p f:= proc(x) local s,L;

%p 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;

%p 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)))

%p end proc:

%p sort(map(f, [$1..5^5-1])); # _Robert Israel_, Jul 06 2018

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

%o (PARI)

%o 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

%o b=list(15000); s=[]; for(n=1, #b, if(#vecsort(eval(Vec(Str(b[n]))),,8)==5, s=concat(s, b[n]))); s

%Y Cf. A235690-A235692, A235694-A235696.

%Y Cf. A235154-A235161.

%K nonn,base

%O 1,1

%A _Colin Barker_, Jan 14 2014

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Last modified April 25 01:35 EDT 2024. Contains 371964 sequences. (Running on oeis4.)