login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The Mersenne primes (A000668) are a subsequence.

LINKS

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

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

Cf. A000668, A061712, A211997.

Sequence in context: A236514 A211997 A127581 * A118883 A061712 A059661

Adjacent sequences:  A278474 A278475 A278476 * A278478 A278479 A278480

KEYWORD

nonn,base

AUTHOR

Joerg Arndt, Nov 23 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 21 07:18 EST 2018. Contains 299390 sequences. (Running on oeis4.)