OFFSET
1,2
COMMENTS
Once there is a k such that k > n and a(k) > n, n can no longer appear in the sequence, otherwise a(k) would be n. - Franklin T. Adams-Watters, Jun 11 2014
If the sum a(1) + a(2) + ... + a(m) is not divisible by m, then m does not belong to this sequence. Sequence A019444 gives a variant of this sequence, where every positive integer is a term. - Max Alekseyev, Jun 11 2014
Positive integers that do not appear in this sequence form A243864.
Is there any index n > 3 such that a(n) <= n? - Max Alekseyev, Jun 13 2014
From Bill McEachen, May 21 2024: (Start)
Conjecture: For n > 1000, a(n) falls within 1% of one of the following six values. a(n) = n, 1.576385*n, 1.788185*n, 2.576385*n, 2.788185*n, or 3.576285*n, using floor at the low bound and ceiling at the high bound, inclusive.
For example, a(1153) = 1836. This is between floor(1.576385 * 1153 * 0.99) and ceiling(1.576385 * 1153 * 1.01). About 90% of values fall in the three lower slopes. (End)
LINKS
Max Alekseyev, Table of n, a(n) for n = 1..100000 (first 1100 terms from Jean-Marc Falcoz)
Éric Angelini, a(n) divides the sum of the first a(n) terms of T, posting to the Sequence Fans Mailing List, Jun 11 2014
Hugo Pfoertner, 1.73*10^6 terms, 7z compressed b-file.
EXAMPLE
1 divides the sum of the first 1 term (yes: 1/1=1)
3 divides the sum of the first 3 terms (yes: 6/3=2)
2 divides the sum of the first 2 terms (yes: 4/2=2)
5 divides the sum of the first 5 terms (yes: 20/5=4)
9 divides the sum of the first 9 terms (yes: 63/9=7)
7 divides the sum of the first 7 terms (yes: 35/7=5)
8 divides the sum of the first 8 terms (yes: 48/8=6)
...
PROG
(PARI) { printA243700() = my( S=Set(), T=[], s=0, m=1, k); for(n=1, 10^5, k=m; while( ((k==n || setsearch(S, n)) && Mod(s+k, n)) || if(k<n, sum(i=1, k, T[i])%k) || setsearch(S, k), k++); S=setunion(S, [k]); T=concat(T, [k]); s+=k; if(s%n, S=setunion(S, [n]); ); while(setsearch(S, m), m++); print1(k, ", "); ) } \\ Max Alekseyev, Jun 13 2014
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
N. J. A. Sloane, Jun 12 2014
EXTENSIONS
First 1100 terms were computed by Jean-Marc Falcoz.
STATUS
approved