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Primes that cannot be written as 1+p+p^k, p prime and k>0.
2

%I #7 Dec 13 2023 12:07:10

%S 2,3,17,29,37,41,43,53,61,71,73,79,89,97,101,103,109,113,127,137,139,

%T 149,151,157,163,173,181,191,193,197,199,211,223,229,233,239,241,251,

%U 257,269,271,277,281,283,293,311,313,317,331,337,349,353,367,373,379

%N Primes that cannot be written as 1+p+p^k, p prime and k>0.

%C A084440(a(n))=0.

%H Robert Israel, <a href="/A084445/b084445.txt">Table of n, a(n) for n = 1..10000</a>

%p N:= 1000: # for terms <= N

%p S:= select(isprime, {2,seq(i,i=3..N,2)}):

%p for i from 1 do

%p p:= ithprime(i);

%p if 2*p+1 > N then break fi;

%p for k from 1 do

%p q:= 1+p+p^k;

%p if q > N then break fi;

%p S:= S minus {q};

%p od;

%p od:

%p sort(convert(S,list)); # _Robert Israel_, Dec 13 2023

%Y Cf. A084441.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, May 26 2003