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%I #19 Nov 15 2015 22:59:04
%S 2,5,13,31,37,61,127,379,439,571,619,739,829,991,1549,3109,3301,3319,
%T 5749,7549,7879,48799
%N Primes p such that p - phi(k)^2 is not prime for 1 <= phi(k)^2 < p.
%C phi is the Euler totient function phi(n) : A000010.
%C A065377 is included in this sequence, and that one is probably finite.
%C No more terms < 10^7. - _Robert Israel_, Nov 15 2015
%e 31 is in the sequence because :
%e 31 - phi(1)^2 = 31 - 1^2 = 30 is composite;
%e 31 - phi(2)^2 = 31 - 1^2 = 30 is composite;
%e 31 - phi(3)^2 = 31 - 2^2 = 27 is composite;
%e 31 - phi(4)^2 = 31 - 2^2 = 27 is composite;
%e 31 - phi(5)^2 = 31 - 4^2 = 15 is composite;
%e 31 - phi(6)^2 = 31 - 2^2 = 27 is the last composite because phi(7)^2 = 6^2 > 31.
%p with(numtheory):for n from 1 to 10000 do:ii:=0:p:=ithprime(n):for k from 1 to p while(p-phi(k)^2>0) do: if type(p- phi(k)^2,prime) =true then ii:=1:else fi:od:if ii=0 then printf(`%d, `,p):else fi:od:
%Y Cf. A000010, A065377.
%K nonn,more
%O 1,1
%A _Michel Lagneau_, Sep 15 2012
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