A095222 (Concatenation of T(n)+1..T(n+1)) mod (concatenation of T(n-1)+1..T(n)), where T(k) is the k-th triangular number, A000217(k).

0, 19, 22, 52785, 459136846, 77032955851, 17865523926168, 1689623507805373, 118763391490664275, 34129170492806856511, 3616977859402101826424, 614427099275584124069065, 34445463838393113230619233, 2480185781714663029796564541499860

Offset: 1

Author

Amarnath Murthy, Jun 10 2004

Keywords

• base
• nonn
• less

Examples

			a(3) = 78910 mod 456 = 22.
From _Jon E. Schoenfield_, Feb 23 2021: (Start)
.
      concatenation of  concatenation of
   n   T(n-1)+1..T(n)    T(n)+1..T(n+1)    a(n)
  --  ----------------  ----------------  -----
   1                 1                23      0
   2                23               456     19
   3               456             78910     22
   4             78910        1112131415  52785
(End)
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A000217, A053067.

Programs

Mathematica

ccat[a_,b_]:=FromDigits[Flatten[IntegerDigits/@Range[a,b]]]; modc[n_]: = Module[{w=(n(n-1))/2+1,x=(n(n+1))/2,y,z},y=x+1;z=2x-w+2; Mod[ccat[y,z], ccat[w,x]]]; Array[modc,20] (* Harvey P. Dale, Nov 27 2012 *)

Formula

a(n) = A053067(n+1) mod A053067(n). - Hagen von Eitzen, Jun 17 2009

Extensions

More terms from Hagen von Eitzen, Jun 17 2009

a(14) from Harvey P. Dale, Nov 27 2012