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

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..10001

Index entries for Hofstadter-type sequences

Formula

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

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

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 *)

Prog

(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)))))))
(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

Crossrefs

Cf. A005185, A284173.

Partial sums of A283467.

Sequence in context: A214780 A024174 A008739 * A025695 A025694 A022796

Adjacent sequences: A280703 A280704 A280705 * A280707 A280708 A280709

Keyword

nonn

Author

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

Status

approved