A278477 Primes that set a new record for the Hamming weight.

2, 3, 7, 23, 31, 127, 383, 991, 2039, 3583, 6143, 8191, 63487, 129023, 131071, 522239, 524287, 1966079, 4128767, 14680063, 33546239, 67108351, 201064447, 260046847, 536739839, 1073479679, 2147483647, 8581545983, 16911433727

Offset: 1

Author

Joerg Arndt, Nov 23 2016

Keywords

• nonn
• base

Comments

The Mersenne primes (A000668) are a subsequence.

Links

• Robert Israel, Table of n, a(n) for n = 1..3301

Crossrefs

Cf. A000668, A061712, A211997.

Programs

Maple

M:= 40: # to use A061712(1..M)
A061712:= proc(n) local d,c,cands;
  for d from 0 do
    cands:= map(t -> 2^(n+d)-1 - add(2^(n-1+d-j), j=t),
        combinat:-choose([$1..n-2+d], d));
    for c in cands do if  isprime(c) then return c fi od
  od
end proc:
A061712(1):= 2:
R:= map(A061712, [$1..M]):
R[select(t -> R[t] < `if`(isprime(2^(M+1)-1), 2^(M+1)-1, 2^(M+2)+2^M-1) and R[t] = min(R[t..-1]), [$1..nops(R)])]; # Robert Israel, Nov 23 2016

PARI

{my(h=0);forprime(p=2,10^11,my(t=hammingweight(p));if(t>h,print1(p,", ");h=t));}