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A250311 Numbers which produce primes if their prime factors, one by one, are prepended, inserted or appended. 3

%I

%S 49,131,133,149,151,157,169,173,179,191,197,199,223,233,239,247,277,

%T 281,283,293,313,331,337,361,367,383,397,401,409,419,421,431,439,443,

%U 457,463,467,469,481,503,547,553,571,577,587,589,607,641,643,659,673,679,701

%N Numbers which produce primes if their prime factors, one by one, are prepended, inserted or appended.

%H Paolo P. Lava, <a href="/A250311/b250311.txt">Table of n, a(n) for n = 1..1000</a>

%e Prime factors of a(1) = 49 are 7, 7 and concat(4,7,9) = 479 is prime.

%e a(2) = 131 is prime and concat(13,131,1) = 131311 is prime, as is concat(1,131,31) = 113131.

%e Prime factors of a(3) = 14383 are 19, 757. Then, concat(1,19,4383) = 1194383 is prime and concat(1438,757,3) = is prime, as is concat(14,757,383) = 14757383.

%p with(numtheory): P:=proc(q) local a,b,c,f,g,h,j,k,n;

%p for n from 1 by 2 to q do a:=ifactors(n)[2]; h:=0;

%p for k from 1 to nops(a) do b:=ilog10(a[k][1])+1;

%p for j from 0 to ilog10(n)+1 do f:=(n mod 10^j);

%p if j=0 then c:=n*10^b+a[k][1]; else g:=a[k][1]*10^(ilog10(f)+1)+f;

%p c:=trunc(n/10^j)*10^(ilog10(g)+1)+g; fi;

%p if isprime(c) then h:=h+1; break; fi; od;

%p if h=nops(a) then print(n); fi; od; od; end: P(10^6);

%Y CF. A250312.

%K nonn,base,easy

%O 1,1

%A _Paolo P. Lava_, Nov 18 2014

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Last modified October 23 10:07 EDT 2021. Contains 348211 sequences. (Running on oeis4.)