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A319707 Filter sequence which records for primes their residue modulo 6, and for all other numbers assigns a unique number.

%I A319707 #8 Oct 05 2018 11:10:26
%S A319707 1,2,3,4,5,6,7,8,9,10,5,11,7,12,13,14,5,15,7,16,17,18,5,19,20,21,22,
%T A319707 23,5,24,7,25,26,27,28,29,7,30,31,32,5,33,7,34,35,36,5,37,38,39,40,41,
%U A319707 5,42,43,44,45,46,5,47,7,48,49,50,51,52,7,53,54,55,5,56,7,57,58,59,60,61,7,62,63,64,5,65,66,67,68,69,5,70,71,72,73,74,75,76,7,77,78,79,5,80,7,81,82,83,5,84,7,85,86,87,5,88,89,90,91,92,93,94,95
%N A319707 Filter sequence which records for primes their residue modulo 6, and for all other numbers assigns a unique number.
%C A319707 Restricted growth sequence transform of function f defined as f(n) = A010875(n) when n is a prime, otherwise -n.
%C A319707 Primes of the form 6k+5 (A007528) get value 5, and the primes of the form 6k+1 (A002476) get value 7, while for all other n, a(n) is assigned to a unique running count.
%C A319707 For all i, j:
%C A319707   a(i) = a(j) => A010875(i) = A010875(j),
%C A319707   a(i) = a(j) => A305900(i) = A305900(j),
%C A319707   a(i) = a(j) => A319717(i) = A319717(j) => A319716(i) = A319716(j).
%H A319707 Antti Karttunen, <a href="/A319707/b319707.txt">Table of n, a(n) for n = 1..100000</a>
%o A319707 (PARI)
%o A319707 up_to = 100000;
%o A319707 rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
%o A319707 A319707aux(n) = if(isprime(n),(n%6),-n);
%o A319707 v319707 = rgs_transform(vector(up_to,n,A319707aux(n)));
%o A319707 A319707(n) = v319707[n];
%Y A319707 Cf. A319716, A319717.
%Y A319707 Cf. A007528 (positions of 5's), A002476 (positions of 7's).
%Y A319707 Cf. also A319704.
%Y A319707 Differs from A319716 for the first time at n=121.
%K A319707 nonn
%O A319707 1,2
%A A319707 _Antti Karttunen_, Oct 04 2018