A087346 -id:A087346 - cp's OEIS frontend

A088116 Let n = abc..., where a, b, c, are digits of n. a(n) = abc...+bac...+c*ab...+..., i.e., a(n) = sum, over all the digits, of the product (number obtained by deleting a digit multiplied by the deleted digit).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 98

Offset: 0

Amarnath Murthy, Sep 25 2003

First 100 terms (for all two digit numbers) match with that of A069816. A088116(10a + b) = 2ab = (a+b)^2 - (a^2 + b^2) = A069816(10a + b).

The first known fixed points, after zero, are numbers of the forms 36*10^k and 1314*10^k for k >= 0. All have 9 as the sum of their digits. Calculated up to n = 10^10. - Stéphane Rézel, Jul 31 2019

			a(1234) = 234 + 2*134 + 3*124 + 4*123 = 1366.

Jinyuan Wang, Table of n, a(n) for n = 0..10000

Cf. A069816, A087346, A088117.

Join[{0},Table[Total[IntegerDigits[n]Table[FromDigits[Drop[ IntegerDigits[ n],{d}]],{d,IntegerLength[n]}]],{n,100}]] (* Harvey P. Dale, Dec 23 2021 *)

a(n) = {v=digits(n);sum(k=1,#v,v[k]*(n\10^(#v-k+1)*10^(#v-k)+n%10^(#v-k)));} \\ Jinyuan Wang, Aug 01 2019

More terms from David Wasserman, May 10 2005

Offset 0 from Stéphane Rézel, Jul 31 2019

cp's OEIS Frontend

A088116 Let n = abc..., where a, b, c, are digits of n. a(n) = abc...+bac...+c*ab...+..., i.e., a(n) = sum, over all the digits, of the product (number obtained by deleting a digit multiplied by the deleted digit).

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cp's OEIS Frontend

A088116 Let n = abc..., where a, b, c, are digits of n. a(n) = a*bc...+b*ac...+c*ab...+..., i.e., a(n) = sum, over all the digits, of the product (number obtained by deleting a digit multiplied by the deleted digit).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

A088116 Let n = abc..., where a, b, c, are digits of n. a(n) = abc...+bac...+c*ab...+..., i.e., a(n) = sum, over all the digits, of the product (number obtained by deleting a digit multiplied by the deleted digit).