Primes that set a new record for the Hamming weight.

Terms

a(0) =2a(1) =3a(2) =7a(3) =23a(4) =31a(5) =127a(6) =383a(7) =991a(8) =2039a(9) =3583a(10) =6143a(11) =8191a(12) =63487a(13) =129023a(14) =131071a(15) =522239a(16) =524287a(17) =1966079a(18) =4128767a(19) =14680063a(20) =33546239a(21) =67108351a(22) =201064447a(23) =260046847a(24) =536739839a(25) =1073479679a(26) =2147483647a(27) =8581545983a(28) =16911433727