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%I #11 Dec 13 2023 15:16:20
%S 0,0,1,2,2,1,0,1,1,0,2,0,0,0,1,0,1,0,1,0,0,0,1,0,0,0,0,1,0,0,0,2,0,0,
%T 0,0,0,0,1,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,
%U 1,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0,0,0,0,0,0,1,0,0
%N Number of ways to write the n-th prime as 1+p+p^k, p prime and k>0.
%C a(A084441(n))>0, a(A084442(n))=1, a(A084443(n))=0.
%H Robert Israel, <a href="/A084440/b084440.txt">Table of n, a(n) for n = 1..10000</a>
%e a(11)=2: prime(11) = 31 = 1+5+5^2 = 1+3+3^3.
%p N:= 200:
%p V:= Vector(N):
%p P:= [seq(ithprime(i),i=1..N)]:
%p for i from 1 to N do
%p p:= P[i];
%p for k from 1 do
%p q:= 1+p+p^k;
%p if q > P[N] then break fi;
%p r:= ListTools:-BinarySearch(P,q);
%p if r > 0 then V[r]:= V[r]+1 fi;
%p od od:
%p convert(V,list); # _Robert Israel_, Dec 13 2023
%Y Cf. A084441, A084442, A084443.
%K nonn
%O 1,4
%A _Reinhard Zumkeller_, May 26 2003
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