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A319350 Filter sequence which records the number of cyclotomic cosets of 2 mod p for odd primes p, and for any other number assigns a unique number.

%I A319350 #12 Sep 26 2018 16:24:02
%S A319350 1,2,3,4,3,5,6,7,8,9,3,10,3,11,12,13,6,14,3,15,16,17,6,18,19,20,21,22,
%T A319350 3,23,24,25,26,27,28,29,3,30,31,32,6,33,34,35,36,37,6,38,39,40,41,42,
%U A319350 3,43,44,45,46,47,3,48,3,49,50,51,52,53,3,54,55,56,6,57,58,59,60,61,62,63,6,64,65,66,3,67,68,69,70,71,58,72,73,74,75,76,77,78,6,79,80,81,3,82,6
%N A319350 Filter sequence which records the number of cyclotomic cosets of 2 mod p for odd primes p, and for any other number assigns a unique number.
%C A319350 Restricted growth sequence transform of function f defined as f(n) = A006694((n-1)/2) when n is an odd prime, otherwise -n.
%C A319350 For all i, j:
%C A319350   a(i) = a(j) => A305801(i) = A305801(j),
%C A319350   a(i) = a(j) => A319351(i) = A319351(j).
%H A319350 Antti Karttunen, <a href="/A319350/b319350.txt">Table of n, a(n) for n = 1..100000</a>
%e A319350 a(3) = a(5) = a(11) = a(13) = a(19) = a(29) = a(37) because 3, 5, 11, 13, 19, 29, 37 are primes p for which A006694((p-1)/2) = 1 (are in A001122).
%e A319350 a(7) = a(17) = a(23) = a(41) = a(47) because 7, 17, 23, 41, 47 are primes p for which A006694((p-1)/2) = 2 (are in A115591).
%o A319350 (PARI)
%o A319350 up_to = 100000;
%o A319350 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 A319350 A319350aux(n) = if((n<=2)||!isprime(n),n,-((n-1)/znorder(Mod(2, n))));
%o A319350 v319350 = rgs_transform(vector(up_to,n,A319350aux(n)));
%o A319350 A319350(n) = v319350[n];
%Y A319350 Cf. A001917, A006694, A286573, A305801, A319351.
%Y A319350 Cf. A001122 (positions of 3's), A115591 (positions of 6's).
%Y A319350 Cf. also A319704, A319705, A319706.
%K A319350 nonn
%O A319350 1,2
%A A319350 _Antti Karttunen_, Sep 26 2018