A095292 -id:A095292 - cp's OEIS frontend

A095282 Primes whose binary-expansion ends with an even number of 1's.

2, 3, 11, 19, 43, 47, 59, 67, 79, 83, 107, 131, 139, 163, 179, 191, 211, 227, 239, 251, 271, 283, 307, 331, 347, 367, 379, 419, 431, 443, 463, 467, 491, 499, 523, 547, 563, 571, 587, 619, 643, 659, 683, 691, 719, 739, 751, 787, 811, 827, 859

Offset: 1

Antti Karttunen, Jun 04 2004

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
A. Karttunen and J. Moyer, C-program for computing the initial terms of this sequence

Intersection of A000040 & (complement of A079523). Complement of A095283 in A000040. Cf. A027699, A095292.

q:= proc(n) local i, l, r; l, r:= convert(n, base, 2), 0;
      for i to nops(l) while l[i]=1 do r:=r+1 od; is(r, even)
    end:
select(q, [ithprime(i)$i=1..200])[];  # Alois P. Heinz, Dec 15 2019

been1Q[n_]:=Module[{c=Split[IntegerDigits[n,2]][[-1]]},c[[1]]==1&&EvenQ[ Length[ c]]]; Join[{2},Select[Prime[Range[150]],been1Q]] (* Harvey P. Dale, Dec 14 2019 *)

is(n)=valuation(n+1,2)%2==0 && isprime(n) \\ Charles R Greathouse IV, Oct 09 2013

A095293 Number of A095283-primes in range ]2^n,2^(n+1)].

Original entry on oeis.org

0, 2, 1, 4, 4, 9, 14, 29, 52, 90, 167, 312, 577, 1072, 2026, 3776, 7177, 13585, 25726, 49125, 93569, 178735, 342381, 657180, 1262818, 2430501, 4684999, 9040931, 17470670, 33798206, 65455531, 126889351, 246216909

Offset: 1

Antti Karttunen, Jun 04 2004

nonn

As expected, the ratio a(n)/A095292(n) seems to approach 2: 0, 0, 1, 4, 1.33333, 2.25, 1.55556, 2.07143, 2.26087, 1.91489, 1.89773, 2.05263, 1.95593, 1.98519, 2.01793, 1.95344, 2.00924, 1.99633, 1.99287, 2.0083, 2.00075, 1.99746, 1.99841, 1.99971, 2.00034, 2.00001, 2.00018, 1.99977, 1.99971, 1.99997, 2.00004, 1.99995, 2.00003

A. Karttunen and J. Moyer: C-program for computing the initial terms of this sequence
Index entries for sequences related to occurrences of various subsets of primes in range 2^n,2^(n+1)

a(n) = A036378(n)-A095292(n). Cf. A095005.

a(n)=my(s);forprime(p=2^n+1,2^(n+1), s+=valuation(p+1, 2)%2); s \\ Charles R Greathouse IV, Oct 09 2013

cp's OEIS Frontend

A095282 Primes whose binary-expansion ends with an even number of 1's.

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