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A316918 For any k, the cumulative sum a(1) + a(2) + a(3) + ... + a(k) starts with a(k). Lexicographic first sequence of positive integers without duplicate terms having this property and extending itself forever. 3
61, 6, 7, 8, 9, 10, 1, 11, 12, 13, 15, 16, 18, 20, 2, 23, 25, 28, 31, 3, 35, 39, 43, 4, 48, 54, 5, 60, 67, 74, 83, 92, 102, 113, 126, 140, 14, 157, 174, 17, 196, 19, 220, 22, 246, 24, 276, 27, 310, 345, 34, 387, 430, 477, 530, 53, 595, 661, 66, 742, 75, 833, 84, 85, 944, 95, 96, 97, 98, 99, 100, 101, 1125, 1250, 1389, 1544 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The authors conjecture that it is impossible to extend the sequence forever if a(1) < 61.

With a(1) = 60, for instance, we will be stuck with the integer 5:

60,6,7,8,9,10,1,11,12,13,15,16,18,20,2,23,25,28,31,3,35,39,43,4,48,54,5 STOP (no unused integer can extend the sequence).

See here the sequence starting with a(1) = 60 and the cumulative sums:

60,6, 7, 8, 9, 10, 1,  11, 12, 13, 15, 16, 18, 20, 2,  23, 25, 28, 31, 3,  35,

60,66,73,81,90,100,101,112,124,137,152,167,185,205,207,230,255,283,314,317,352,

(the two lines above continue here):

39, 43, 4,  48, 54, 5, STOP

391,434,438,486,540,545.

LINKS

Jean-Marc Falcoz, Table of n, a(n) for n = 1..5004

EXAMPLE

Here are the first terms of the sequence:

61,6,7,8,9,10,1,11,12,13,15,16,18,20,2,23,25,...

and here are the cumulative sums:

61,67,74,82,91,101,102,113,125,138,153,169,187,207,209, 232,257,...

If we align the a(n)s and the cumulative sums, we see that those always begin with the integer above it:

  61,6, 7, 8, 9, 10, 1,  11, 12, 13, 15, 16, 18, 20, 2,  23, 25,...

  61,67,74,82,91,101,102,113,125,138,153,169,187,207,209,232,257,...

CROSSREFS

Sequence in context: A345224 A198189 A102600 * A077331 A106426 A106416

Adjacent sequences:  A316915 A316916 A316917 * A316919 A316920 A316921

KEYWORD

base,nonn

AUTHOR

Eric Angelini and Jean-Marc Falcoz, Jul 16 2018

STATUS

approved

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Last modified May 16 11:35 EDT 2022. Contains 353704 sequences. (Running on oeis4.)