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

Author

Bill McEachen, Aug 06 2024

Keywords

• nonn

Comments

Sequence closely parallel to A000295.

Examples

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

Crossrefs

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

Programs

Mathematica

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

PARI

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

Formula

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

Extensions

More terms from Amiram Eldar, Aug 06 2024