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

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, 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, 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

Offset

1,2

Comments

Restricted growth sequence transform of function f defined as f(n) = A010875(n) when n is a prime, otherwise -n.

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.

For all i, j:

a(i) = a(j) => A010875(i) = A010875(j),

a(i) = a(j) => A305900(i) = A305900(j),

a(i) = a(j) => A319717(i) = A319717(j) => A319716(i) = A319716(j).

Links

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

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; };
A319707aux(n) = if(isprime(n), (n%6), -n);
v319707 = rgs_transform(vector(up_to, n, A319707aux(n)));
A319707(n) = v319707[n];

Crossrefs

Cf. A319716, A319717.

Cf. A007528 (positions of 5's), A002476 (positions of 7's).

Cf. also A319704.

Differs from A319716 for the first time at n=121.

Sequence in context: A320117 A319996 A319716 * A319717 A292266 A292267

Adjacent sequences: A319704 A319705 A319706 * A319708 A319709 A319710

Keyword

nonn

Author

Antti Karttunen, Oct 04 2018

Status

approved