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A216168 Composite numbers and 1 which yield a prime whenever a 7 is inserted anywhere in them, including at the beginning or end. 3

%I #11 Sep 08 2022 08:46:03

%S 1,9,27,33,39,57,87,159,177,187,603,717,753,949,1257,1707,2277,2367,

%T 4317,4623,4779,4797,5773,6757,6777,7017,7471,7479,7747,7797,7813,

%U 7977,8797,9777,9987,10777,11757,17679,28269,28437,29779,34177,34771,40059,41721

%N Composite numbers and 1 which yield a prime whenever a 7 is inserted anywhere in them, including at the beginning or end.

%H Paolo P. Lava, <a href="/A216168/b216168.txt">Table of n, a(n) for n = 1..150</a>

%e 4623 is not prime but 46237, 46273, 46723, 47623 and 74623 are all primes.

%p with(numtheory);

%p A216168:=proc(q,x)

%p local a,b,c,i,n,ok;

%p for n from 1 to q do

%p if not isprime(n) then

%p a:=n; b:=0; while a>0 do b:=b+1; a:=trunc(a/10); od; a:=n; ok:=1;

%p for i from 0 to b do c:=a+9*10^i*trunc(a/10^i)+10^i*x;

%p if not isprime(c) then ok:=0; break; fi;

%p od;

%p if ok=1 then print(n); fi;

%p fi;

%p od; end:

%p A216168(1000,7);

%o (Magma) [n: n in [1..50000] | not IsPrime(n) and forall{m: t in [0..#Intseq(n)] | IsPrime(m) where m is (Floor(n/10^t)*10+7)*10^t+n mod 10^t}]; // _Bruno Berselli_, Sep 03 2012

%Y Cf. A068673, A068674, A068677, A068679, A069246, A215417, A215419-A215421, A216165-A216167, A216169.

%K nonn,base

%O 1,2

%A _Paolo P. Lava_, Sep 03 2012

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Last modified March 29 10:59 EDT 2024. Contains 371277 sequences. (Running on oeis4.)