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A359734
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Lexicographically earliest sequence of distinct nonnegative integers such that the sequence A051699(a(n)) (distance from the nearest prime) has the same sequence of digits.
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2
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1, 10, 2, 0, 3, 26, 9, 119, 532, 4, 6, 896, 118, 34, 15, 93, 121, 531, 898, 205, 8, 12, 533, 50, 117, 14, 122, 1078, 56, 16, 21, 18, 144, 64, 20, 895, 1138, 899, 25, 5, 186, 1077, 22, 27, 204, 76, 86, 206, 7, 24, 28, 120, 30, 123, 32, 33, 35, 36, 11, 300
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OFFSET
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0,2
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COMMENTS
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In the definition, "has the same digits" means that the concatenation of the terms yields the same string of digits, for the sequence a(.) and the sequence A051699(a(.)).
Conjectured to be a permutation of the nonnegative integers. The inverse permutation would start (3, 0, 2, 4, 9, 39, 10, 48, 20, 6, 1, 58, 21, 75, 25, 14, ...).
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LINKS
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Eric Angelini, Digit-spines, personal blog "Cinquante signes" on blogspot.com, Jan. 11, 2023.
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EXAMPLE
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Below, row "p" lists the closest prime to a(n) and row "d" the absolute difference |a(n)-p|. We have the same sequence of digits in rows a (this sequence) and d:
n : 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 ...
a : 1 10 2 0 3 26 9 119 532 4 6 896 118 34 15 ...
p : 2 11 2 2 3 23 7 113 523 3 5 887 113 31 13 ...
d : 1 1 0 2 0 3 2 6 9 1 1 9 5 3 2 ...
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PROG
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(PARI) spine(f, N=20, S=[], d=[], md = n -> if(n, digits(n), [0])) = { vector(N, n, my(m, j=1); for(k=0, oo, setsearch(S, k) && next; while( f(j) < k, j++); m = md(min(m = f(j) - k, iferr(k - f(j-1), E, m))); if(m == concat(d, md(k))[1..#m], d = concat(d, md(k))[#m+1 .. -1]; m=k; break)); S = setunion(S, [m]); m)}
spine(prime, 200) \\ 200 terms of this sequence
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CROSSREFS
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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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