|
%I #20 Feb 09 2023 21:55:25
%S 1,2,13,103,107,1007,1036,1019,1013,1049,1079,1237,10099,10013,10135,
%T 10123,10039,10127,10079,10238,10234,10235,10139,10478,12349,12347,
%U 10378,12359,14579,10789,100336,10237,12389,23579,10279,100136,12379,10379,100267,13789
%N a(n) is the least number with exactly n permutations of digits that are primes.
%C From _Robert Israel_, Feb 07 2023: (Start)
%C Permutations that have leading zeros are included, in contrast to A046890 where they are not.
%C If neither A046890(n) nor a(n) have the digit 0, then they are equal. (End)
%H Robert Israel, <a href="/A046893/b046893.txt">Table of n, a(n) for n = 0..1477</a>
%p g:= proc(d) local x,d1,y;
%p [seq(seq(seq(x*10^d + y, y = [0,h(x,d1)]),d1=0..d-1),x=1..9)]
%p end proc:
%p g(0):= [$0..9]:
%p h:= proc(x0, d) local y,z; option remember;
%p seq(seq(y*10^d+z, z = [procname(y,d-1)]),y=x0..9)
%p end proc:
%p for x0 from 1 to 9 do h(x0,0):= $x0 .. 9 od:
%p f:= proc(n) local t,L,d,P,i;
%p t:= 0;
%p L:= convert(n,base,10); d:= nops(L);
%p for P in combinat:-permute(L) do
%p if isprime(add(P[i]*10^(i-1),i=1..d)) then t:= t+1 fi
%p od;
%p t
%p end proc:
%p N:= 100: # for a(0)..a(N)
%p V:= Array(0..N): count:= 0:
%p for d from 0 while count < N+1 do
%p for i in g(d) while count < N+1 do
%p v:= f(i);
%p if v <= N then
%p if V[v] = 0 then V[v]:= i; count:= count+1; fi;
%p fi
%p od od:
%p convert(V,list); # _Robert Israel_, Feb 07 2023
%t a = Table[0, {40}]; Do[b = Count[ PrimeQ[ FromDigits /@ Permutations[ IntegerDigits[n]]], True]; If[b < 40 && a[[b + 1]] == 0, a[[b + 1]] = n; Print[b, " ", n]], {n, 1, 110000}]
%o (Python)
%o from sympy import isprime
%o from sympy.utilities.iterables import multiset_permutations as mp
%o from itertools import count, islice, combinations_with_replacement as mc
%o def nd(d): yield from ("".join((f,)+m) for f in "123456789" for m in mc("0123456789", d-1))
%o def c(s): return sum(1 for p in mp(s) if p[0]!="0" and isprime(int("".join(p))))
%o def agen(): # generator of sequence terms
%o n, adict = 0, dict()
%o for digs in count(1):
%o for s in nd(digs):
%o v = c(s)
%o if v not in adict: adict[v] = int(s)
%o while n in adict: yield adict[n]; n += 1
%o print(list(islice(agen(), 40))) # _Michael S. Branicky_, Feb 08 2023
%Y Cf. A039999, A046890. All terms are in A179239.
%K nonn,base,look
%O 0,2
%A _David W. Wilson_
|
