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.

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

Offset

1,2

Comments

Restricted growth sequence transform of function f defined as f(n) = A006694((n-1)/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((p-1)/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((p-1)/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, -((n-1)/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: A323373 A332826 A353840 * A336855 A329895 A342552

Adjacent sequences: A319347 A319348 A319349 * A319351 A319352 A319353

Keyword

nonn

Author

Antti Karttunen, Sep 26 2018

Status

approved