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A299869
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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) = 6.
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2
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6, 60, 594, 5945, 59454, 594535, 5945351, 59453514, 594535135, 5945351351, 59453513510, 594535135104, 5945351351035, 59453513510351, 594535135103509, 5945351351035091, 59453513510350914, 594535135103509135, 5945351351035091351, 59453513510350913508, 594535135103509135082, 5945351351035091350820
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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) = 6 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) ~ 0.66*10^n, a(n) ~ 0.59*10^n. See A300000 for the proof. - M. F. Hasler, Feb 22 2018
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EXAMPLE
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6 + 60 = 66 which is the concatenation of 6 and 6.
6 + 60 + 594 = 660 which is the concatenation of 6, 6 and 0.
6 + 60 + 594 + 5945 = 6605 which is the concatenation of 6, 6, 0 and 5.
From n = 3 on, a(n) can be computed directly as c(n) - c(n-1), cf. formula: a(3) = 660 - 66 = 594, a(4) = 6605 - 660 = 5945, etc. - M. F. Hasler, Feb 22 2018
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PROG
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(PARI) a(n, show=1, a=6, c=a, d=[a])={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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