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

Author

Antti Karttunen, Oct 04 2018

Keywords

• nonn

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

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.

Programs

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];