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 A108581 #8 Nov 08 2024 08:37:16 %S A108581 1,3,3,3,6,6,6,6,6,6,10,10,10,10,10,10,10,10,10,10,15,15,15,15,15,15, %T A108581 15,15,15,15,15,15,15,15,15,21,21,21,21,21,21,21,21,21,21,21,21,21,21, %U A108581 21,21,21,21,21,21,21,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28 %N A108581 Positive triangular numbers repeated their own number of times. %C A108581 In terms of the repetition convolution operator #, where (sequence A) # (sequence B) = the sequence consisting of A(n) copies of B(n), then this sequence is the repetition self-convolution (A000217(n)-0) # (A000217(n)-0). Over the set of positive infinite integer sequences, # gives a nonassociative noncommutative groupoid with a left identity (A000012) but no right identity, where the left identity is also a right nullifier and idempotent. %F A108581 a(1) = 1, for n>1: a(A000217(n)-1) = a(A000217(n)) = ... = a(A000217(n+1)-2) = A000217(n). %F A108581 a(n) = A000217(m+1) if 6n>m(m+1)(m+2) and a(n) = A000217(m) otherwise where m = floor((6n)^(1/3)). - _Chai Wah Wu_, Nov 07 2024 %o A108581 (Python) %o A108581 from sympy import integer_nthroot %o A108581 def A108581(n): return (r:=(m:=integer_nthroot(k:=6*n,3)[0])+(k>m*(m+1)*(m+2)))*(r+1)>>1 # _Chai Wah Wu_, Nov 07 2024 %Y A108581 Cf. A000217, A002024, A072649, A074279. %K A108581 easy,nonn %O A108581 1,2 %A A108581 _Jonathan Vos Post_, Jul 25 2005