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%I #16 Jan 27 2021 10:26:11
%S 0,1,1,3,3,1,3,3,1,9,3,13,1,9,7,9,5,3,15,5,3,3,1,3,3,11,3,5,3,9,5,3,3,
%T 19,1,3,13,5,5,3,9,5,3,3,5,9,3,15,5,7,11,13,9,33,1,9,3,5,13,9,5,3,3,
%U 19,1,3,3,15,5,39,7,11,13,5,7,9,39,1,7,1,7
%N Number of composites of the form n^2 + 1 between two successive primes of this form.
%C a(n) is the number of composites of A134406 between A002496(n) and A002496(n+1).
%H Michel Lagneau, <a href="/A206400/b206400.txt">Table of n, a(n) for n = 1..10000</a>
%e a(4) = 3 because there exist 3 composite numbers of the form n^2+1 : {50, 65, 82} between A002496(4) = 37 and A002496(5) = 101.
%p i:=0:for n from 2 to 1000 do:x:=n^2+1:if type (x,prime)=true then printf(`%d, `,i):i:=0:else i:=i+1:fi:od:
%t cfn2[{a_,b_}]:=Count[Range[a+1,b-1],_?(IntegerQ[Sqrt[#-1]]&)]; cfn2/@ Partition[ Select[Prime[Range[50000]],IntegerQ[Sqrt[#-1]]&],2,1] (* _Harvey P. Dale_, Jan 13 2019 *)
%o (PARI) c=0; for(n=2,1e9, !ispseudoprime(n^2+1) & c++ & next; print1(c","); c=0) \\ _M. F. Hasler_, Feb 07 2012
%Y Cf. A002522, A002496, A134406.
%K nonn
%O 1,4
%A _Michel Lagneau_, Feb 07 2012
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