A088116 -id:A088116 - cp's OEIS frontend

A087346 a(n) = A088116(100+n).

11, 22, 33, 44, 55, 66, 77, 88, 99, 20, 33, 46, 59, 72, 85, 98, 111, 124, 137, 40, 55, 70, 85, 100, 115, 130, 145, 160, 175, 60, 77, 94, 111, 128, 145, 162, 179, 196, 213, 80, 99, 118, 137, 156, 175, 194, 213, 232, 251, 100, 121, 142, 163, 184, 205, 226, 247, 268

Offset: 1

Amarnath Murthy, Sep 07 2003

			a(2) = A088116(102) = 1*2+0*12+2*10 = 22.

Edited and extended by David Wasserman, May 10 2005

A088117 Let the decimal expansion of n be abcd...; then a(n) = (abcd... + bacd... + cabd... + dabc... + ...) + (abcd... + bcad... + cdab... + ...) + ... . That is, a(n) = sum over all the digit strings of the product (number obtained by deleting a digit string) (deleted digit string).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 0, 7, 14, 21, 28, 35, 42, 49, 56, 63, 0, 8, 16, 24, 32, 40, 48, 56, 64, 72, 0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 0, 11

Offset: 0

Amarnath Murthy, Sep 25 2003

Each substring is used in only product.

a(n) = 0 for 0 <= n <= 10.

			a(1234) = (1*234 + 2*134 + 3*124 + 4*123) + (12*34 + 23*14) = 2096.
a(12345) = (1*2345 + 2*1345 + 3*1245 + 4*1235 + 5*1234) + (12*345 + 15*234 + 23*145 + 34*125 + 45*123) = 40650.

Alois P. Heinz, Table of n, a(n) for n = 0..20000

Cf. A007954, A088116.

Different from A035930, A171765, A257850.

a:= n-> (s-> add(add(parse(s[i..j])*parse(cat(s[1..i-1],
    s[j+1..length(s)])), i=1..j), j=1..length(s)-1))(""||n):
seq(a(n), n=0..120);  # Alois P. Heinz, May 22 2021

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jul 14 2007

a(0)=0 inserted and examples corrected by Alois P. Heinz, May 22 2021

cp's OEIS Frontend

A087346 a(n) = A088116(100+n).

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A088117 Let the decimal expansion of n be abcd...; then a(n) = (abcd... + bacd... + cabd... + dabc... + ...) + (abcd... + bcad... + cdab... + ...) + ... . That is, a(n) = sum over all the digit strings of the product (number obtained by deleting a digit string) (deleted digit string).

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Maple

Extensions

cp's OEIS Frontend

A087346 a(n) = A088116(100+n).

Views

Author

Keywords

Examples

Extensions

A088117 Let the decimal expansion of n be abcd...; then a(n) = (a*bcd... + b*acd... + c*abd... + d*abc... + ...) + (ab*cd... + bc*ad... + cd*ab... + ...) + ... . That is, a(n) = sum over all the digit strings of the product (number obtained by deleting a digit string) * (deleted digit string).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Extensions

A088117 Let the decimal expansion of n be abcd...; then a(n) = (abcd... + bacd... + cabd... + dabc... + ...) + (abcd... + bcad... + cdab... + ...) + ... . That is, a(n) = sum over all the digit strings of the product (number obtained by deleting a digit string) (deleted digit string).