A375235 Records of A112591.

1, 6, 12, 28, 58, 126, 252, 506, 1012, 2042, 4082, 8190, 16366, 32742, 65518, 131056, 262114, 524280, 1048554, 2097146, 4194278, 8388594, 16777208, 33554390, 67108858, 134217716, 268435396, 536870852, 1073741814, 2147483614, 4294967284, 8589934580, 17179869158

Offset

1,2

Comments

Sequence closely parallel to A000295.

Links

Table of n, a(n) for n=1..33.

Formula

a(n) = previous_prime(2^n) XOR next_prime(2^n) = A112591(A014234(n)) for n > 1.

Example

The first term of A112591 = 1 is a record and is a(1). The next A112591 value > 1 is 6 which is a(2).

Mathematica

a[n_] := BitXor @@ NextPrime[2^n, {-1, 1}]; a[1] = 1; Array[a, 33] (* Amiram Eldar, Aug 08 2024 *)

Prog

(PARI) a(n)= if(n==1, 1, bitxor(precprime(2^n), nextprime(2^n) ))

Crossrefs

Cf. A000295, A014210 (primes where records occur), A014234, A112591.

Sequence in context: A146005 A325812 A323652 * A223346 A109510 A034715

Adjacent sequences: A375232 A375233 A375234 * A375236 A375237 A375238

Keyword

nonn

Author

Bill McEachen, Aug 06 2024

Extensions

More terms from Amiram Eldar, Aug 06 2024

Status

approved