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A249299
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Numbers j such that the sum of the first j terms, Sum_{k=1..j} a(k), is not in this list.
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2
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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
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OFFSET
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1,1
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COMMENTS
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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, ... .
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LINKS
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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
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EXAMPLE
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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.
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PROG
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(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))}
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CROSSREFS
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Sequence in context: A039257 A345914 A039198 * A039149 A039081 A195128
Adjacent sequences: A249296 A249297 A249298 * A249300 A249301 A249302
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KEYWORD
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nonn
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AUTHOR
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Eric Angelini and M. F. Hasler, Oct 24 2014
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STATUS
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approved
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