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URL: https://oeis.org/A278477

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A278477
Primes that set a new record for the Hamming weight.
1
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
1,1
COMMENTS
The Mersenne primes (A000668) are a subsequence.
LINKS
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
PROG
(PARI) {my(h=0); forprime(p=2, 10^11, my(t=hammingweight(p)); if(t>h, print1(p, ", "); h=t)); }
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Joerg Arndt, Nov 23 2016
STATUS
approved