A293428 a(0) = 1; and for n > 0, a(n) = a(n-1) + (A008966(4n+1) - A107078(4n+3)).

1, 2, 2, 3, 4, 5, 4, 5, 6, 7, 8, 8, 8, 9, 10, 10, 11, 12, 12, 13, 13, 14, 15, 16, 16, 17, 18, 19, 20, 20, 20, 20, 21, 21, 22, 23, 23, 24, 24, 25, 26, 27, 26, 26, 27, 28, 29, 29, 30, 31, 32, 32, 33, 34, 35, 36, 36, 37, 38, 39, 39, 39, 40, 41, 42, 42, 43, 44, 44, 44, 45, 46, 46, 47, 47, 48, 49, 50, 50, 51, 52, 52, 53, 53

Offset

0,2

Comments

After a(0)=1, each term a(n) is either (a) one more than its predecessor, in case 4n+1 and 4n+3 are both squarefree, (b) stays same if only the other one is squarefree, or (c) decreases by one if neither 4n+1 nor 4n+3 are squarefree.

Links

Antti Karttunen, Table of n, a(n) for n = 0..10000

Formula

a(0) = 1; and for n > 0, a(n) = a(n-1) + -1+(A008966(4n+1)+A008966(4n+3)).

Or for n > 0, a(n) = a(n-1) + (A008966(4n+1) - A107078(4n+3)).

Prog

(Scheme, with memoization-macro definec)
(definec (A293428 n) (if (zero? n) 1 (+ -1 (A008966 (+ 1 (* 4 n))) (A008966 (+ 3 (* 4 n))) (A293428 (- n 1)))))

Crossrefs

Cf. A008966, A107078, A293229, A293429.

Cf. also A293517.

Sequence in context: A030584 A030564 A205114 * A281487 A224401 A252462

Adjacent sequences: A293425 A293426 A293427 * A293429 A293430 A293431

Keyword

nonn

Author

Antti Karttunen, Oct 16 2017

Status

approved