%I #25 Feb 06 2021 22:38:33
%S 10,32,56,712,920,1130,1342,1556,1772,1990,21110,23132,25156,27182,
%T 29210,31240,33272,35306,37342,39380,41420,43462,45506,47552,49600,
%U 51650,53702,55756,57812,59870,61930,63992,651056,671122,691190,711260,731332,751406,771482
%N Concatenation of sum n+(n+1) and product n*(n+1) in decimal.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Concatenation.html">Concatenation</a>
%F a(n) = (2n+1)*10^b + n^2 + n, where b is length of n^2 + n.
%e For n = 0: n+1 = 1; 0+1 is 1 and 0*1 is 0. So concatenate to a(0) = 10.
%e For n = 1: n+1 = 2; 1+2 is 3 and 1*2 is 2. So a(1) = 32.
%e For n = 10: n+1 = 11; 10+11 is 21 and 10*11 is 110. So a(10) = 21110.
%t Table[(2n+1)*10^Length[IntegerDigits[n^2+n]]+n^2+n,{n,0,38}] (* _Stefano Spezia_, Jan 29 2021 *)
%o (Python)
%o def concatenate(n):
%o return (2*n+1)*10**len(str(n**2+n))+ n**2+n
%Y Cf. A002378, A005408.
%K base,nonn
%O 0,1
%A _Ercan Isik_, Jan 27 2021
%E More terms from _Stefano Spezia_, Jan 29 2021