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A359734 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. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
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, ...).
LINKS
Eric Angelini, Digit-spines, personal blog "Cinquante signes" on blogspot.com, Jan. 11, 2023.
EXAMPLE
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 ...
PROG
(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
CROSSREFS
Cf. A051699 (distance from the nearest prime), A000040 (the primes).
Cf. A359736, A359737 (similar for squares and Fibonacci numbers).
Sequence in context: A288020 A071938 A261942 * A057603 A040097 A010174
KEYWORD
nonn,base
AUTHOR
M. F. Hasler and Eric Angelini, Jan 12 2023
STATUS
approved

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Last modified May 26 04:29 EDT 2024. Contains 372807 sequences. (Running on oeis4.)