Mark Nandor - cp's OEIS frontend

User: Mark Nandor

Mark Nandor has authored 2 sequences.

A166749 Numbers that are the sum or product of two numbers, such that the sum and product have reversed digits.

0, 4, 18, 27, 49, 72, 81, 94, 499, 994, 4999, 9994, 49999, 99994, 499999, 999994, 4999999, 9999994, 49999999, 99999994, 499999999, 999999994, 4999999999, 9999999994, 49999999999, 99999999994, 499999999999, 999999999994, 4999999999999, 9999999999994, 49999999999999

Offset: 1

Mark Nandor, Oct 21 2009

Note that 0 and 4 are their own reversed-digit sums and products, since 0+0=0*0=0 and 2+2=2*2=4. The pattern of some number of nines and then a four, and a four and some number of nines, continues indefinitely.

These are in fact all the solutions, shown by a case-by-case analysis. - Wang Pok Lo, Dec 24 2018

			For instance, 9*9=81 and 9+9=18 are terms; 3*24=72 and 3+24=27 are terms too.

W. P. Lo and Y. Paz, On finding all positive integers a,b such that b±a and ab are palindromic, arXiv:1812.08807 [math.HO] (2018).

Do[If[IntegerDigits[x y] == Reverse[IntegerDigits[x + y]], Print[{x, y, x + y, x y}]], {x, 0, 20}, {y, x, 100000}] or a[1]=0;a[2]=4;a[3]=18;a[4]=27;a[5]=49;a[6]=72;a[7]=81;a[8]=94 a[n_] := a[n] = If[OddQ[n], 5*10^((n + 1)/2 - 3) - 1, 10^(n/2 - 2) - 6]

For n>8, a(n)=5*10^((n+1)/2 - 3) - 1 if n odd; a(n)=10^(n/2 - 2) - 6 if n even.

A110883 Sum of consecutive digits in the decimal expansion of Pi.

Original entry on oeis.org

4, 5, 5, 6, 14, 11, 8, 11, 8, 8, 13, 17, 16, 16, 12, 5, 5, 11, 12, 10, 8, 8, 10, 7, 6, 11, 11, 5, 9, 16, 14, 5, 2, 10, 16, 12, 5, 10, 16, 8, 7, 15, 12, 12, 18, 12, 10, 12, 6, 1, 5, 13, 10, 2, 9, 16, 11, 13, 13, 8, 9, 14, 11, 5, 3, 7, 15, 9, 7, 10, 4, 6, 8, 10, 14, 8, 2, 8, 17, 18, 17, 14, 8

Offset: 1

Blaine J. Deal and Mark Nandor, Sep 19 2005

			a(1)=3+1 = 4, a(2)=1+4 = 5, a(3)=4+1 = 5, a(4)=1+5 = 6, a(5)=5+9 = 14

Paolo Xausa, Table of n, a(n) for n = 1..10000
Blaine Deal, Sequence puzzle posting at Clifford Pickover forum. [Broken link]
Blaine Deal, Home Page.
Albert Frank and Philippe Jacqueroux, International Contest, 2001. Item 25.

Cf. A000796.

listlength = 100; Table[IntegerDigits[IntegerPart[10^listlength Pi]][[i]] + IntegerDigits[IntegerPart[10^listlength (Pi - 3.0`100)]][[i]], {i, 1, listlength}]
(* Second program: *)
Total[Partition[First[RealDigits[Pi, 10, 100]], 2, 1], {2}] (* Paolo Xausa, Aug 22 2025 *)

a(n) = p(n) + p(n+1) where p(n) is the n-th digit of Pi (see sequence A000796).

a(n) = A000796(n) + A000796(n+1).

Typo in formula fixed by Zak Seidov, Jan 02 2014

cp's OEIS Frontend

User: Mark Nandor

A166749 Numbers that are the sum or product of two numbers, such that the sum and product have reversed digits.

Views

Author

Keywords

Comments

Examples

Links

Programs

Mathematica

Formula