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A299865
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The sum of the first n terms of the sequence is the concatenation of the first n digits of the sequence, and a(1) = 2.
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9
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2, 20, 198, 1981, 19818, 198179, 1981783, 19817838, 198178379, 1981783783, 19817837830, 198178378308, 1981783783079, 19817837830783, 198178378307837, 1981783783078363, 19817837830783638, 198178378307836379, 1981783783078363783, 19817837830783637836, 198178378307836378362, 1981783783078363783612
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OFFSET
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1,1
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COMMENTS
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The sequence starts with a(1) = 2 and is always extended with the smallest integer not yet present in the sequence and not leading to a contradiction.
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LINKS
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FORMULA
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a(n) = c(n) - c(n-1), where c(n) = concatenation of the first n digits, c(n) ~ 0.22*10^n, a(n) ~ 0.198*10^n. See A300000 for the proof. - M. F. Hasler, Feb 22 2018
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EXAMPLE
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2 + 20 = 22 which is the concatenation of 2 and 2.
2 + 20 + 198 = 220 which is the concatenation of 2, 2 and 0.
2 + 20 + 198 + 1981 = 2201 which is the concatenation of 2, 2, 0 and 1.
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PROG
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(PARI) a(n, show=1, a=2, c=a, d=[c])={for(n=2, n, show&&print1(a", "); a=-c+c=c*10+d[1]; d=concat(d[^1], if(n>2, digits(a)))); a} \\ M. F. Hasler, Feb 22 2018
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CROSSREFS
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A300000 is the lexicographically first sequence of this type, with a(1) = 1.
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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