A256908 Initialization a(n)=0 for all n; if a(n)=0, a(n+kp)=n where p=prime(n) and k=0,1,2,...

1, 2, 1, 4, 1, 6, 1, 2, 1, 10, 1, 12, 1, 2, 1, 5, 1, 3, 1, 2, 1, 22, 1, 7, 1, 2, 1, 3, 1, 30, 1, 2, 1, 34, 1, 36, 1, 2, 1, 40, 1, 11, 1, 2, 1, 4, 1, 3, 1, 2, 1, 52, 1, 13, 1, 2, 1, 3, 1, 4, 1, 2, 1, 64, 1, 66, 1, 2, 1, 70, 1, 72, 1, 2, 1, 17, 1, 3, 1, 2, 1, 5

Offset

1,2

Comments

Conjecture: there is an infinity of numbers n such that a(n)=n.

Links

Michel Lagneau, Table of n, a(n) for n = 1..10000

Example

n=1 => prime(1)=2 and a(1+2k)=1 => a(1)=a(3)=a(5)=... =1;
n=2 => prime(2)=3 and a(2+3k)=2 => a(2)=a(8)=... =2 (the element a(5) is already in the sequence);
n=3 => prime(3)=5 and a(3+5k)=3 => a(18)=3 (the elements a(n) for n<18 are already in the sequence), a(28)=3, a(48)=3,...

Maple

with(numtheory):nn:=500:T:=array(1..nn):
  for i from 1 to nn do:
   T[i]:=0:
  od:
    for n from 1 to nn do:
    p:=ithprime(n):
     for m from n by p to nn do:
      if T[m]=0 then T[m]:=n:
      else
      fi:
     od:
    od:
    print(T):

Crossrefs

Sequence in context: A276094 A247339 A281071 * A346466 A258409 A060680

Adjacent sequences: A256905 A256906 A256907 * A256909 A256910 A256911

Keyword

nonn

Author

Michel Lagneau, Apr 12 2015

Status

approved