

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
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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, Digitspines, 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(j1), 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



KEYWORD

nonn,base


AUTHOR



STATUS

approved



