

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.


3



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, 3, 23, 24, 25, 26, 27, 28, 29, 3, 30, 31, 32, 6, 33, 34, 35, 36, 37, 6, 38, 39, 40, 41, 42, 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
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OFFSET

1,2


COMMENTS

Restricted growth sequence transform of function f defined as f(n) = A006694((n1)/2) when n is an odd prime, otherwise n.
For all i, j:
a(i) = a(j) => A305801(i) = A305801(j),
a(i) = a(j) => A319351(i) = A319351(j).


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..100000


EXAMPLE

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((p1)/2) = 1 (are in A001122).
a(7) = a(17) = a(23) = a(41) = a(47) because 7, 17, 23, 41, 47 are primes p for which A006694((p1)/2) = 2 (are in A115591).


PROG

(PARI)
up_to = 100000;
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; };
A319350aux(n) = if((n<=2)!isprime(n), n, ((n1)/znorder(Mod(2, n))));
v319350 = rgs_transform(vector(up_to, n, A319350aux(n)));
A319350(n) = v319350[n];


CROSSREFS

Cf. A001917, A006694, A286573, A305801, A319351.
Cf. A001122 (positions of 3's), A115591 (positions of 6's).
Cf. also A319704, A319705, A319706.
Sequence in context: A319351 A323373 A332826 * A336855 A329895 A342552
Adjacent sequences: A319347 A319348 A319349 * A319351 A319352 A319353


KEYWORD

nonn


AUTHOR

Antti Karttunen, Sep 26 2018


STATUS

approved



