cp's OEIS Frontend

A085942 Write digit reversal of n below n. Then a(n) = the sum of the product of digits in the same column.

%I A085942 #21 May 22 2021 03:12:16
%S A085942 0,1,4,9,16,25,36,49,64,81,0,2,4,6,8,10,12,14,16,18,0,4,8,12,16,20,24,
%T A085942 28,32,36,0,6,12,18,24,30,36,42,48,54,0,8,16,24,32,40,48,56,64,72,0,
%U A085942 10,20,30,40,50,60,70,80,90,0,12,24,36,48,60,72,84,96,108,0,14,28,42,56,70,84
%N A085942 Write digit reversal of n below n. Then a(n) = the sum of the product of digits in the same column.
%C A085942 a(n) = sum of the products of r-th most significant digit and the r-th least significant digit, the sum being taken over all the digits of n.
%C A085942 If the number of digits in n is even then a(n) is also even.
%C A085942 a(36) = 36.
%H A085942 Rémy Sigrist, <a href="/A085942/b085942.txt">Table of n, a(n) for n = 0..10000</a>
%e A085942 a(4) = 4*4 = 16.
%e A085942 a(123) = 10: 123
%e A085942 ............ 321 (1*3 +2*2 +3*1 = 10).
%e A085942 a(1203) = 1*3 + 2*0 + 0*2 +3*1 = 6.
%e A085942 a(1234) = 1*4 +2*3 + 3*2 +4*1 = 20.
%t A085942 dr[n_]:=Module[{idn=IntegerDigits[n]},Total[Times@@@Transpose[Join[{idn, Reverse[idn]}]]]]; Array[dr,80] (* _Harvey P. Dale_, May 03 2011 *)
%o A085942 (PARI) a(n) = { my (d=digits(n)); d*Colrev(d) } \\ _Rémy Sigrist_, May 21 2021
%Y A085942 Cf. A111707.
%K A085942 base,easy,nonn
%O A085942 0,3
%A A085942 _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jul 14 2003
%E A085942 More terms from _David Wasserman_, Feb 14 2005
%E A085942 Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_, May 31 2007
%E A085942 a(0) = 0 prepended by _Rémy Sigrist_, May 21 2021