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%I #32 Dec 07 2019 12:18:26
%S 3,4,5,10,14,16,40,46,100,145,149,251,340,373,406,424,439,466,539,556,
%T 571,575,617,619,628,629,655,676,689,724,760,779,794,899,901,941,970,
%U 989,1019,1055,1070,1076,1183,1213,1226,1231,1258,1270,1285,1331,1340
%N Numbers n with property that the concatenation of their anti-divisors is a prime.
%C Similar to A120712 which uses the proper divisors of n.
%H Klaus Brockhaus <a href="/A191647/b191647.txt">Table of n, a(n) for n = 1..1000</a> (first 250 terms from Paolo P. Lava)
%e The anti-divisors of 40 are 3, 9, 16, 27, and 391627 is prime, hence 40 is in the sequence.
%p P:=proc(i) local a,b,c,d,k,n,s,v; v:=array(1..200000);
%p for n from 3 by 1 to i do k:=2; b:=0;
%p while k<n do if (k mod 2)=0 then
%p if (n mod k)>0 and (2*n mod k)=0 then b:=b+1; v[b]:=k; fi;
%p else
%p if (n mod k)>0 and (((2*n-1) mod k)=0 or ((2*n+1) mod k)=0) then
%p b:=b+1; v[b]:=k; fi; fi; k:=k+1; od; a:=v[1];
%p for s from 2 to b do a:=a*10^floor(1+evalf(log10(v[s])))+v[s]; od;
%p if isprime(a) then print(n); fi;
%p od; end: P(10^6);
%t antiDivisors[n_Integer] := Cases[Range[2, n - 1], _?(Abs[Mod[n, #] - #/2] < 1 &)]; a191647[n_Integer] := Select[Range[n],
%t PrimeQ[FromDigits[Flatten[IntegerDigits /@ antiDivisors[#]]]] &]; a191647[1350] (* _Michael De Vlieger_, Aug 09 2014, "antiDivisors" after _Harvey P. Dale_ at A066272 *)
%o (Python)
%o from sympy import isprime
%o [n for n in range(3,10**4) if isprime(int(''.join([str(d) for d in range(2,n) if n%d and 2*n%d in [d-1,0,1]])))] # _Chai Wah Wu_, Aug 08 2014
%Y Cf. A037279, A066272, A106708, A120712, A120716, A191648.
%K nonn,base
%O 1,1
%A _Paolo P. Lava_, Jun 10 2011
%E a(618) corrected in b-file by _Paolo P. Lava_, Feb 28 2018
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