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A267097 a(n) = number of 4k+1 primes among first n primes; least monotonic left inverse of A080147.

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%I A267097 #15 May 02 2025 03:33:29
%S A267097 0,0,1,1,1,2,3,3,3,4,4,5,6,6,6,7,7,8,8,8,9,9,9,10,11,12,12,12,13,14,
%T A267097 14,14,15,15,16,16,17,17,17,18,18,19,19,20,21,21,21,21,21,22,23,23,24,
%U A267097 24,25,25,26,26,27,28,28,29,29,29,30,31,31,32,32,33,34,34,34,35,35,35,36,37,38,39,39,40,40,41
%N A267097 a(n) = number of 4k+1 primes among first n primes; least monotonic left inverse of A080147.
%C A267097 a(n) = number of 4k+1 primes (A002144) among primes in range 2 .. A000040(n).
%H A267097 Antti Karttunen, <a href="/A267097/b267097.txt">Table of n, a(n) for n = 1..65537</a>
%F A267097 Other identities. For all n >= 1:
%F A267097 a(A080147(n)) = n.
%F A267097 a(n) + A267098(n) = n-1.
%t A267097 a[n_]:=Length[Select[Prime[Range[n]],IntegerQ[(#-1)/4] &]]; Array[a,84] (* _Stefano Spezia_, May 01 2025 *)
%o A267097 (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o A267097 (define A267097 (LEFTINV-LEASTMONO 1 1 A080147))
%Y A267097 Cf. A000040, A002144, A080147, A267098.
%Y A267097 Cf. also A267101.
%K A267097 nonn
%O A267097 1,6
%A A267097 _Antti Karttunen_, Feb 01 2016