This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A359736 #11 Dec 21 2024 18:20:50 %S A359736 0,10,1,2,6,42,20,7,11,4,56,3,5,21,30,43,12,31,14,8,13,9,29,19,15,18, %T A359736 22,17,24,32,72,26,28,90,23,91,35,109,37,41,48,73,27,34,50,57,38,40, %U A359736 33,47,71,51,62,55,66,89,112,16,79,39,130,63,46,44,65,25,135 %N A359736 Lexicographically earliest sequence of distinct nonnegative integers such that the sequence d(n) = dist(a(n), SQUARES) has the same sequence of digits. %C A359736 In the definition, dist(a(n), SQUARES) = A053188(a(n)) is the distance of a(n) from the nearest square. "... has the same digits" means that the concatenation of the terms yields the same string of digits, for the sequence a(.) and the sequence d(.). %C A359736 Conjectured to be a permutation of the nonnegative integers. The inverse permutation would start (0, 2, 3, 11, 9, 12, 4, 7, 19, 21, 1, 8, 16, 20, 18, 24, ...) %H A359736 Eric Angelini, <a href="https://cinquantesignes.blogspot.com/2023/01/digit-spines.html">Digit-spines</a>, personal blog "Cinquante signes" on blogspot.com, Jan. 11, 2023. %H A359736 Eric Angelini, <a href="/A359736/a359736.pdf">Digit-spines</a>, personal blog "Cinquante signes" on blogspot.com, Jan. 11, 2023. [Cached copy] %e A359736 Below, row "s" lists the closest square to a(n) and row "d" the absolute difference |a(n)-s|. We have the same sequence of digits in rows a (this sequence) and d: %e A359736 n : 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 ... %e A359736 a : 0 10 1 2 6 42 20 7 11 4 56 3 5 21 30 ... %e A359736 s : 0 9 1 1 4 36 16 9 9 4 49 4 6 25 25 ... %e A359736 d : 0 1 0 1 2 6 4 2 2 0 7 1 1 4 5 ... %o A359736 (PARI) spine(x->x^2, 200) \\ See A359734 for spine() %Y A359736 Cf. A053188 (distance from the nearest square), A000290 (the squares). %Y A359736 Cf. A359734, A359737 (similar for primes and Fibonacci numbers). %K A359736 nonn,base %O A359736 0,2 %A A359736 _M. F. Hasler_ and _Eric Angelini_, Jan 12 2023