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A245203 Least k>=0 such that A004767(n) = 4n+3 is the mean of primes 4(n-k)+3 and 4(n+k)+3; or -1 if no such k exists.

%I A245203 #13 Dec 23 2024 14:53:43
%S A245203 0,0,0,1,0,0,1,0,3,2,0,0,2,3,0,1,0,0,1,0,0,4,3,3,7,0,0,7,3,3,4,0,0,1,
%T A245203 0,9,4,0,6,2,0,0,2,6,0,4,6,0,1,0,6,4,0,6,2,0,0,2,9,0,5,6,0,4,12,0,1,0,
%U A245203 9,7,0,6,5,3,12,16,0,0,8,3,15,5,0,6,2,9,0,17,6,0,1,0,3,2,0,0,14,27,9,5,9,6,7,12,0,10,15,0,1,0,0,4,3,3,5,0,0,2,3,0,1,0,0,1,0,0,4
%N A245203 Least k>=0 such that A004767(n) = 4n+3 is the mean of primes 4(n-k)+3 and 4(n+k)+3; or -1 if no such k exists.
%C A245203 It has been conjectured that A004767(n) = 4n+3 is either prime or the mean of two primes in sequence A004767.
%C A245203 See A244952 and A245205 for record values and indices of these records. Some of these records are a(97)=27, a(1139)=120, a(10181)=225, a(93124)=435, a(864901)=894, ...
%H A245203 M. F. Hasler, <a href="/A245203/b245203.txt">Table of n, a(n) for n = 0..9999</a>
%H A245203 Mike T.W., <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2014-July/013297.html">Could I add this conjecture to A004767: 4*n+3?</a>, SeqFan list, Jul 10 2014
%o A245203 (PARI) a(n)={-!forstep(k=0,n=4*n+3,4,isprime(n-k)&&isprime(n+k)&&return(k\4))}
%Y A245203 Cf. A002145.
%K A245203 nonn
%O A245203 0,9
%A A245203 _M. F. Hasler_, Jul 13 2014