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A126084 a(n) = XOR of first n primes. 5
0, 2, 1, 4, 3, 8, 5, 20, 7, 16, 13, 18, 55, 30, 53, 26, 47, 20, 41, 106, 45, 100, 43, 120, 33, 64, 37, 66, 41, 68, 53, 74, 201, 64, 203, 94, 201, 84, 247, 80, 253, 78, 251, 68, 133, 64, 135, 84, 139, 104, 141, 100, 139, 122, 129, 384, 135, 394, 133, 400, 137, 402, 183, 388, 179 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The values at odd positive indices are even and the values at even positive indices are odd.

Does this sequence contain any zeros for n > 0? Probabilistically, one would expect so; but none in first 10000 terms. - Franklin T. Adams-Watters, Jul 17 2011

None below 1.5 * 10^11: any prime p such that a(pi(p)) = 0 is 43 bits or longer. Heuristic chances that a prime below 2^100 yields 0 are about 45%. Note that an n-bit prime can yield 0 only if a(pi(p)) is odd, where p is the smallest n-bit prime. That is, for n > 1, there are no zeros from pi(2^n) to pi(2^(n+1)) if A007053(n) is even. - Charles R Greathouse IV, Jul 17 2011

LINKS

Franklin T. Adams-Watters, Table of n, a(n) for n = 0..10000

FORMULA

a(0) = 0; a(n) = a(n-1) XOR prime(n).

EXAMPLE

a(4) = 3 because ((2 XOR 3) XOR 5) XOR 7 = (1 XOR 5) XOR 7 = 4 XOR 7 = 3

[Or, in base 2]

((10 XOR 11) XOR 101) XOR 111 = (1 XOR 101) XOR 111 = 100 XOR 111 = 11

MATHEMATICA

Module[{nn=70, prs}, prs=Prime[Range[nn]]; Table[BitXor@@Take[prs, n], {n, 0, nn}]] (* Harvey P. Dale, Jun 23 2016 *)

PROG

(PARI) al(n)=local(m); vector(n, k, m=bitxor(m, prime(k))) /* Produces a vector without a(0) = 0; Franklin T. Adams-Watters, Jul 17 2011 */

(PARI) v=primes(300); for(i=2, #v, v[i]=bitxor(v[i], v[i-1])); concat(0, v) \\ Charles R Greathouse IV, Aug 26 2014

(PARI) q=0; forprime(p=2, 313, print1(q, ", "); q=bitxor(q, p)) /* Klaus Brockhaus, Mar 06 2007; adapted by Rémy Sigrist, Oct 23 2017 */

CROSSREFS

Cf. A003815, A004767, A112591.

Sequence in context: A008347 A112387 A193174 * A294022 A076077 A152194

Adjacent sequences:  A126081 A126082 A126083 * A126085 A126086 A126087

KEYWORD

nonn,base

AUTHOR

Esko Ranta, Mar 02 2007

EXTENSIONS

More terms from Klaus Brockhaus, Mar 06 2007

Edited by N. J. A. Sloane, Oct 22 2017 (merging old entry A193174 with this).

Edited by Rémy Sigrist, Oct 23 2017

STATUS

approved

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Last modified April 11 15:49 EDT 2021. Contains 342886 sequences. (Running on oeis4.)