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

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, 28, 32, 36, 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 0, 8, 16, 24, 32, 40, 48, 56, 64, 72, 0, 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

Offset: 0

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jul 14 2003

Keywords

• base
• easy
• nonn

Comments

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.

If the number of digits in n is even then a(n) is also even.

a(36) = 36.

Examples

			a(4) = 4*4 = 16.
a(123) = 10: 123
............ 321 (1*3 +2*2 +3*1 = 10).
a(1203) = 1*3 + 2*0 + 0*2 +3*1 = 6.
a(1234) = 1*4 +2*3 + 3*2 +4*1 = 20.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A111707.

Programs

Mathematica

dr[n_]:=Module[{idn=IntegerDigits[n]},Total[Times@@@Transpose[Join[{idn, Reverse[idn]}]]]]; Array[dr,80] (* Harvey P. Dale, May 03 2011 *)

PARI

a(n) = { my (d=digits(n)); d*Colrev(d) } \\ Rémy Sigrist, May 21 2021

Extensions

More terms from David Wasserman, Feb 14 2005

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 31 2007

a(0) = 0 prepended by Rémy Sigrist, May 21 2021