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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
1, 9, 27, 33, 39, 57, 87, 159, 177, 187, 603, 717, 753, 949, 1257, 1707, 2277, 2367, 4317, 4623, 4779, 4797, 5773, 6757, 6777, 7017, 7471, 7479, 7747, 7797, 7813, 7977, 8797, 9777, 9987, 10777, 11757, 17679, 28269, 28437, 29779, 34177, 34771, 40059, 41721
OFFSET
1,2
LINKS
EXAMPLE
4623 is not prime but 46237, 46273, 46723, 47623 and 74623 are all primes.
MAPLE
with(numtheory);
A216168:=proc(q, x)
local a, b, c, i, n, ok;
for n from 1 to q do
if not isprime(n) then
a:=n; b:=0; while a>0 do b:=b+1; a:=trunc(a/10); od; a:=n; ok:=1;
for i from 0 to b do c:=a+9*10^i*trunc(a/10^i)+10^i*x;
if not isprime(c) then ok:=0; break; fi;
od;
if ok=1 then print(n); fi;
fi;
od; end:
A216168(1000, 7);
PROG
(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
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, Sep 03 2012
STATUS
approved