A257247 - OEIS

%I #16 Apr 19 2015 22:41:47

%S 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,

%T 69,74,78,81,88,89,91,93,97,99,101,102,114,116,120,123,126,134,141,

%U 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

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

%C 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.

%C 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).

%H Antti Karttunen, <a href="/A257247/b257247.txt">Table of n, a(n) for n = 1..289</a>

%e 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.

%o (Scheme, with _Antti Karttunen_'s IntSeq-library, three alternative definitions)

%o (define A257247 (MATCHING-POS 1 1 (lambda (n) (= (A257245 n) (A257246 n)))))

%o (define A257247 (MATCHING-POS 1 1 (lambda (n) (= (A006530 (A256393 (+ n n -1))) (A020639 (A256393 (+ n n)))))))

%o (define A257247 (MATCHING-POS 1 1 (lambda (n) (= (gcd (A256393 (+ -1 n n)) (A256393 (+ n n))) (gcd (A256393 (+ n n)) (A256393 (+ 1 n n)))))))

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

%K nonn

%O 1,2

%A _Antti Karttunen_, Apr 19 2015