A257247 Numbers n such that A257245(n) = A257246(n), or equally, where A257244(2n) = A257244(2n-1).

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 14, 17, 20, 23, 27, 31, 36, 49, 51, 56, 59, 63, 66, 67, 69, 74, 78, 81, 88, 89, 91, 93, 97, 99, 101, 102, 114, 116, 120, 123, 126, 134, 141, 144, 146, 148, 152, 161, 163, 172, 173, 179, 192, 194, 195, 202, 207, 214, 219, 223, 227, 235, 240, 242, 246, 250, 252, 256

Offset

1,2

Comments

The sequence gives numbers n such that A257244(2n) = A257244(2n-1), in other words, where the difference A256393(2n+1) - A256393(2n) is equal to the difference A256393(2n) - A256393(2n-1). This is equal to the condition that A256393(2n-1) and A256393(2n) share the same unique prime factor that A256393(2n) and A256393(2n+1) also share.

Also, numbers n such that the largest prime factor (A006530) of A256393(2n - 1) is equal to the smallest prime factor (A020639) of A256393(2n).

Links

Antti Karttunen, Table of n, a(n) for n = 1..289

Example

Terms A256393[3949..3951] = (6299579580, 6299580499, 6299581418) factorize as 2*2*3*5*7*19*859*919, 919*919*7459, 2*13*919*263647. We see that gcd(A256393(3949),A256393(3950)) = gcd(A256393(3950),A256393(3951)) = 919, thus 3950/2 = 1975 is included in the sequence.

Prog

(Scheme, with Antti Karttunen's IntSeq-library, three alternative definitions)
(define A257247 (MATCHING-POS 1 1 (lambda (n) (= (A257245 n) (A257246 n)))))
(define A257247 (MATCHING-POS 1 1 (lambda (n) (= (A006530 (A256393 (+ n n -1))) (A020639 (A256393 (+ n n)))))))
(define A257247 (MATCHING-POS 1 1 (lambda (n) (= (gcd (A256393 (+ -1 n n)) (A256393 (+ n n))) (gcd (A256393 (+ n n)) (A256393 (+ 1 n n)))))))

Crossrefs

Cf. A006530, A020639, A256393, A257244, A257245, A257246.

Sequence in context: A059519 A163101 A157465 * A269164 A356899 A230780

Adjacent sequences: A257244 A257245 A257246 * A257248 A257249 A257250

Keyword

nonn

Author

Antti Karttunen, Apr 19 2015

Status

approved