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

0,3

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.

Links

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A111707.

Sequence in context: A169669 A111707 A115300 * A066308 A063462 A098736

Adjacent sequences: A085939 A085940 A085941 * A085943 A085944 A085945

Keyword

base,easy,nonn

Author

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

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

Status

approved