A249299 Numbers j such that the sum of the first j terms, Sum_{k=1..j} a(k), is not in this list.

2, 3, 4, 6, 7, 8, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 77, 78, 79, 80, 81, 82, 83, 84

Offset

1,1

Comments

Sequence A249331 lists the numbers not in this sequence, i.e., 1, 5, 9, 15, 30, 40, 51, 76, 90, 106, 123, 141, 180, 201, 223, 246, 270, 295, ... .

Links

M. F. Hasler, Table of n, a(n) for n = 1..964

E. Angelini, Sum of the a(n) first terms of S is not in S, SeqFan list, Oct 23 2014

Example

The number 1 cannot appear in the sequence, since the sum of the first n=1 terms equals a(1) which is necessarily in the sequence. (Similarly for 0.)
So the smallest number that can be in the sequence is a(1)=2.
There is no (further) restriction on a(2) since 2+a(2) will always be a number not in the set {2, a(2)}. Thus the next larger number, a(2)=3, is also in this list.
The number a(3)=4 is also allowed, but because of a(1)=2 the number a(1)+a(2)=5 is excluded, as well as the number a(1)+a(2)+a(3)=2+3+4=9 because of a(2)=3.

Prog

(PARI) {A249299=[]; A249331=[s=0, 1]; for(n=2, 999, setsearch(A249331, n)&&next; A249299=concat(A249299, n); s+=n; setsearch(A249299, #A249299)&&A249331=concat(A249331, s))}

Crossrefs

Sequence in context: A039257 A345914 A039198 * A039149 A039081 A195128

Adjacent sequences: A249296 A249297 A249298 * A249300 A249301 A249302

Keyword

nonn

Author

Eric Angelini and M. F. Hasler, Oct 24 2014

Status

approved