A336855 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), for all i, j >= 1, where f(p) = p-nextprime(p) for primes p, and f(n) = n for all other numbers.

1, 2, 3, 4, 3, 5, 6, 7, 8, 9, 3, 10, 6, 11, 12, 13, 3, 14, 6, 15, 16, 17, 18, 19, 20, 21, 22, 23, 3, 24, 18, 25, 26, 27, 28, 29, 6, 30, 31, 32, 3, 33, 6, 34, 35, 36, 18, 37, 38, 39, 40, 41, 18, 42, 43, 44, 45, 46, 3, 47, 18, 48, 49, 50, 51, 52, 6, 53, 54, 55, 3, 56, 18, 57, 58, 59, 60, 61, 6, 62, 63, 64, 18, 65, 66

Offset: 1

Author

Antti Karttunen, Aug 09 2020

Keywords

• nonn

Comments

Restricted growth sequence transform of function f defined as: f(n) = -{distance to the next larger prime} when n is a prime, otherwise f(n) = -n.

For all i, j:

a(i) = a(j) => A305801(i) = A305801(j),

a(i) = a(j) => A336852(i) = A336852(j),

a(i) = a(j) => A336853(i) = A336853(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000
• Index entries for primes, gaps between

Crossrefs

Cf. also A001359 (positions of 3's), A305801, A319704, A331304, A336852, A336853.

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; };
A336855aux(n) = if(isprime(n),n-nextprime(1+n),n);
v336855 = rgs_transform(vector(up_to,n,A336855aux(n)));
A336855(n) = v336855[n];