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.

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

Offset: 0

Author

M. F. Hasler and Eric Angelini, Jan 12 2023

Keywords

• nonn
• base

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, ...).

Examples

			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 ...
		

Links

• Eric Angelini, Digit-spines, personal blog "Cinquante signes" on blogspot.com, Jan. 11, 2023.
• Eric Angelini, Digit-spines, personal blog "Cinquante signes" on blogspot.com, Jan. 11, 2023. [Cached copy]

Crossrefs

Cf. A051699 (distance from the nearest prime), A000040 (the primes).

Cf. A359736, A359737 (similar for squares and Fibonacci numbers).

Programs

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