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A250312 Numbers which produce primes if their divisors, one by one, are prepended, inserted or appended.

%I A250312 #10 Nov 25 2014 10:17:50
%S A250312 1,151,157,169,223,277,283,337,361,367,397,409,421,439,457,469,547,
%T A250312 571,577,589,607,643,673,709,757,769,793,871,877,937,1063,1093,1201,
%U A250312 1603,1609,1807,2029,2053,2071,2707,3019,3037,3049,3073,3109,3607,4039,4051,4087
%N A250312 Numbers which produce primes if their divisors, one by one, are prepended, inserted or appended.
%H A250312 Paolo P. Lava, <a href="/A250312/b250312.txt">Table of n, a(n) for n = 1..1000</a>
%e A250312 Divisors of 1 is 1 and concat(1,1) = 11 is prime.
%e A250312 Divisors of 151 are 1, 151. Then concat(151,1) = 1511 is prime, as is concat(1,151) = 1151, and concat(1,151,51) = 115151 is prime.
%e A250312 Divisors of 169 are 1, 13, 169. Then concat(16,1,9) = 1619 is prime, concat(16,13,9) = 16139 is prime, as is concat(1,13,69) = 11369, and concat(1,169,69) = 116969 is prime.
%p A250312 with(numtheory): P:=proc(q) local a,b,c,f,g,h,j,k,n;
%p A250312 for n from 1 by 2 to q do a:=divisors(n); h:=0;
%p A250312 for k from 1 to nops(a) do b:=ilog10(a[k])+1;
%p A250312 for j from 0 to ilog10(n)+1 do f:=(n mod 10^j);
%p A250312 if j=0 then c:=n*10^b+a[k]; else g:=a[k]*10^(ilog10(f)+1)+f;
%p A250312 c:=trunc(n/10^j)*10^(ilog10(g)+1)+g; fi;
%p A250312 if isprime(c) then h:=h+1; break; fi; od;
%p A250312 if h=nops(a) then print(n); fi; od; od; end: P(10^6);
%Y A250312 CF. A250311.
%K A250312 nonn,base,easy
%O A250312 1,2
%A A250312 _Paolo P. Lava_, Nov 18 2014
%E A250312 Inserted a(3), a(16) and a(26) by _Paolo P. Lava_, Nov 21 2014