A365512 a(n) is the least odd prime p such that A000120(n*p) = A000120(n) * A000120(p).

3, 3, 5, 3, 3, 5, 17, 3, 3, 3, 17, 5, 17, 17, 17, 3, 3, 3, 5, 3, 3, 17, 257, 5, 5, 17, 257, 17, 257, 17, 257, 3, 3, 3, 5, 3, 3, 5, 257, 3, 3, 3, 257, 17, 17, 257, 257, 5, 5, 5, 5, 17, 257, 257, 257, 17, 257, 257, 257, 17, 257, 257, 257, 3, 3, 3, 5, 3, 3, 5, 257, 3, 3, 3, 17, 5, 257, 257, 257, 3

Offset

1,1

Comments

a(2*n) = a(n).

a(n) <= A365475(A070939(n)), with a(2^n-1) = A365475(n).

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Index entries for sequences related to binary expansion of n

Example

a(3) = 5 because 5 is an odd prime with A000120(3 * 5) = 4 = A000120(3) * A000120(5) while A000120(3 * 3) = 2 < 4 = A000120(3) * A000120(3).

Maple

g:= n -> convert(convert(n, base, 2), `+`):
f:= proc(n) option remember; local t, S, d, L, B, forbid, i, j, r, q;
  if n::even then return procname(n/2^padic:-ordp(n, 2)) fi;
  L:= convert(n, base, 2);
  t:= convert(L, `+`);
  B:= select(t -> L[t]=1, [$1..nops(L)]);
  forbid:= {seq(seq(B[i]-B[j], j=1..i-1), i=1..nops(B))};
  S[0]:= [1];
  for d from 1 do
    S[d]:= NULL;
    for j from 0 to d-1 do
      if member(d-j, forbid) then next fi;
      for r in S[j] do
        q:= r + 2^d;
        if g(q*n) = t*g(q) then
          if isprime(q) then return q fi;
          S[d]:= S[d], q;
        fi
      od
    od;
    S[d]:= [S[d]];
  od
end proc:
map(f, [$1..100]);

Prog

(PARI) a(n) = my(p=3, h=hammingweight(n)); while (hammingweight(n*p) != h*hammingweight(p), p = nextprime(p+1)); p; \\ Michel Marcus, Sep 08 2023

Crossrefs

Cf. A000120, A070939, A365475.

Sequence in context: A235649 A113965 A162277 * A060397 A352351 A359421

Adjacent sequences: A365509 A365510 A365511 * A365513 A365514 A365515

Keyword

nonn,base

Author

Robert Israel, Sep 07 2023

Status

approved