A027706 - OEIS

A027706

n-th prime has odd number of 1's in binary expansion and (n+1)st prime has even number of 1's.

%I #15 Jun 01 2019 12:44:50

%S 1,6,8,13,15,19,22,25,29,33,37,44,54,58,61,63,65,67,73,75,78,86,88,90,

%T 95,98,100,104,107,113,116,121,123,130,132,136,138,140,145,149,151,

%U 153,158,164,169,172,175,177,181,186,189,193,198,202,205,207,210,212,220

%N n-th prime has odd number of 1's in binary expansion and (n+1)st prime has even number of 1's.

%H Vincenzo Librandi, <a href="/A027706/b027706.txt">Table of n, a(n) for n = 1..2600</a>

%t c[ n_ ] := OddQ[ Count[ IntegerDigits[ n,2 ],1 ] ]; Select[ Range[ 500 ],c[ Prime[ # ] ]&&Not[ c[ Prime[ #+1 ] ] ]& ]

%t SequencePosition[Table[If[OddQ[DigitCount[n,2,1]],1,0],{n,Prime[Range[ 300]]}],{1,0}][[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jun 01 2019 *)

%Y Cf. A027705 (corresponding primes).

%Y Cf. A027702, A027704, A027708.

%K nonn

%O 1,2

%A _N. J. A. Sloane_.

%E More terms from _Erich Friedman_

%E Offset changed by _Michel Marcus_, Mar 29 2018