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A095283 Primes whose binary-expansion ends with an odd number of 1's. 4

%I #17 Jan 03 2022 21:48:45

%S 5,7,13,17,23,29,31,37,41,53,61,71,73,89,97,101,103,109,113,127,137,

%T 149,151,157,167,173,181,193,197,199,223,229,233,241,257,263,269,277,

%U 281,293,311,313,317,337,349,353,359,373,383,389,397,401,409

%N Primes whose binary-expansion ends with an odd number of 1's.

%H Charles R Greathouse IV, <a href="/A095283/b095283.txt">Table of n, a(n) for n = 1..10000</a>

%H A. Karttunen and J. Moyer, <a href="/A095062/a095062.c.txt">C-program for computing the initial terms of this sequence</a>

%p q:= proc(n) local i, l, r; l, r:= convert(n, base, 2), 0;

%p for i to nops(l) while l[i]=1 do r:=r+1 od; is(r, odd)

%p end:

%p select(q, [ithprime(i)$i=1..150])[]; # _Alois P. Heinz_, Dec 15 2019

%t Select[Prime[Range[100]], MatchQ[IntegerDigits[#, 2], {b:(1)..}|{___, 0, b:(1)..} /; OddQ[Length[{b}]]]&] (* _Jean-François Alcover_, Jan 03 2022 *)

%o (PARI) is(n)=valuation(n+1,2)%2 && isprime(n) \\ _Charles R Greathouse IV_, Oct 09 2013

%o (Python)

%o from sympy import isprime

%o def ok(n): b = bin(n); return (len(b)-len(b.rstrip("1")))%2 and isprime(n)

%o print([k for k in range(1, 401) if ok(k)]) # _Michael S. Branicky_, Jan 03 2022

%Y Intersection of A000040 & A079523. Complement of A095282 in A000040. Cf. A027697, A095293.

%K nonn,base,easy

%O 1,1

%A _Antti Karttunen_, Jun 04 2004

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)