A280706 a(n) = Sum_{k=1..n} q(k+1-q(k)), where q(k) = A005185(k); partial sums of A283467.

1, 2, 3, 4, 6, 8, 10, 13, 16, 19, 23, 26, 30, 35, 39, 44, 49, 54, 60, 66, 72, 78, 86, 92, 100, 108, 116, 124, 132, 142, 150, 159, 169, 179, 189, 200, 211, 221, 232, 243, 254, 266, 278, 290, 302, 314, 330, 340, 354, 368, 380, 394, 410, 424, 438, 454, 468, 484, 500, 516, 532, 552, 568, 585, 606, 622, 639, 658, 678, 698, 719, 740

Offset: 1

Author

Antti Karttunen after Altug Alkan's A284173, Mar 22 2017

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10001
• Index entries for Hofstadter-type sequences

Crossrefs

Cf. A005185, A284173.

Partial sums of A283467.

Programs

Mathematica

a[1] = a[2] = 1; a[n_] := a[n] = a[n - a[n - 1]] + a[n - a[n - 2]]; Accumulate@ Table[a[n + 1 - a[n]], {n, 72}] (* Michael De Vlieger, Mar 22 2017 *)

PARI

a(n) = if(n<3, 1, a(n - a(n - 1)) + a(n - a(n - 2)));
for(n=1, 72, print1(sum(k=1, n, a(k + 1 - a(k))),", ")) \\ Indranil Ghosh, Mar 22 2017

Scheme

;; Code for A005185 given under that entry.
;; With memoization-macro definec:
(definec (A280706 n) (if (= 1 n) 1 (+ (A280706 (- n 1)) (A283467 n))))
;; As an explicit sum (slower):
(define (A280706 n) (add (lambda (k) (A005185 (- (+ k 1) (A005185 k)))) 1 n))
;; Implements sum_{i=lowlim..uplim} intfun(i)
(define (add intfun lowlim uplim) (let sumloop ((i lowlim) (res 0)) (cond ((> i uplim) res) (else (sumloop (1+ i) (+ res (intfun i)))))))

Formula

a(1) = 1, for > 1, a(n) = A283467(n) + a(n-1).

A284173(n) = a(n) modulo n.