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A379000 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = 0 if n is prime > 5, with f(n) = n for all other n.

%I A379000 #10 Dec 15 2024 12:11:55
%S A379000 1,2,3,4,5,6,7,8,9,10,7,11,7,12,13,14,7,15,7,16,17,18,7,19,20,21,22,
%T A379000 23,7,24,7,25,26,27,28,29,7,30,31,32,7,33,7,34,35,36,7,37,38,39,40,41,
%U A379000 7,42,43,44,45,46,7,47,7,48,49,50,51,52,7,53,54,55,7,56,7,57,58,59,60,61,7,62,63,64,7,65,66,67,68,69,7,70,71,72,73,74,75,76,7,77,78,79,7
%N A379000 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = 0 if n is prime > 5, with f(n) = n for all other n.
%C A379000 For all i, j:
%C A379000   a(i) = a(j) => A305900(i) = A305900(j) => A305801(i) = A305801(j) => A305800(i) = A305800(j),
%C A379000   a(i) = a(j) => A379001(i) = A379001(j) => A379002(i) = A379002(j),
%C A379000   a(i) = a(j) => A379005(i) = A379005(j).
%H A379000 Antti Karttunen, <a href="/A379000/b379000.txt">Table of n, a(n) for n = 1..100000</a>
%F A379000 For n < 7, a(n) = n, for primes > 5, a(n) = 7, and for composite n > 7, a(n) = 4+n-A000720(n).
%o A379000 (PARI) A379000(n) = if(n<=7, n, if(isprime(n), 7, 4+n-primepi(n)));
%Y A379000 Cf. A000720.
%Y A379000 Cf. A112765, A305800, A305801, A305900, A379001, A379002, A379005.
%K A379000 nonn
%O A379000 1,2
%A A379000 _Antti Karttunen_, Dec 15 2024