A136601 -id:A136601 - cp's OEIS frontend

A066957 a(n) = number of ways of placing '+' and '-' among the digits 123456789 so that the result of the expression is n, '-' before 1 IS allowed.

22, 43, 18, 41, 18, 40, 24, 39, 18, 46, 17, 38, 27, 38, 24, 43, 18, 39, 23, 37, 23, 43, 25, 36, 32, 36, 25, 44, 25, 35, 34, 31, 26, 37, 24, 35, 32, 32, 27, 37, 31, 26, 34, 34, 29, 42, 27, 27, 35, 26, 28, 35, 29, 33, 30, 26, 23, 29, 32, 25, 33, 30, 24, 34, 22, 26, 32, 30, 25

Offset: 0

Miklos SZABO (mike(AT)ludens.elte.hu), Feb 01 2002

A066957(9)=46 is the largest term; A066957(456789)=2 is the last term greater than 1; a(n)=0 for n>123456789; 1715 terms are greater than 0; a(A136601(n))=0; a(A136602(n))>0; a(A136603(n))=1; partial sums are A136604. - Reinhard Zumkeller, Jan 12 2008

R. Zumkeller, Table of n, a(n) for n = 0..10000
R. Zumkeller, Illustration of initial terms

Cf. A066956.

A136602 Nonnegative numbers that can be obtained by inserting minus and plus-signs in 123456789.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72

Offset: 1

Reinhard Zumkeller, Jan 12 2008

A066957(a(n)) > 0; complement of A136601; A136603 is a subsequence;
a(n) = n-1 for n <= 211 = A136601(1).
The sequence is finite: a(1715) = 123456789 is the last term.

R. Zumkeller, Table of n, a(n) for n = 1..1715

A136603 Positive numbers having a unique representation by inserting minus and plus-signs in 123456789.

Original entry on oeis.org

176, 191, 194, 196, 209, 213, 215, 217, 223, 237, 253, 259, 263, 272, 274, 275, 289, 290, 292, 293, 295, 305, 307, 308, 353, 361, 367, 379, 380, 381, 382, 386, 392, 399, 401, 405, 415, 416, 418, 419, 427, 443, 461, 463, 467, 475, 477, 479, 481, 490, 491

Offset: 1

Reinhard Zumkeller, Jan 12 2008

A066957(a(n)) = 1; subsequence of A136601;

the sequence is finite with 869 terms.

			a(1) = 176 = 1 - 2 + 34 + 56 + 78 + 9;
a(2) = 191 = 123 + 4 + 56 + 7 - 8 + 9;
a(3) = 194 = 1 - 2 + 34 + 5 + 67 + 89;
a(4) = 196 = -1 + 2 + 34 + 5 + 67 + 89;
a(5) = 209 = 1 + 234 + 56 + 7 - 89;
a(6) = 213 = 123 + 4 + 5 - 6 + 78 + 9;
a(7) = 215 = 123 + 4 - 5 + 6 + 78 + 9;
a(8) = 217 = 123 - 4 + 5 + 6 + 78 + 9;
a(9) = 223 = -1 + 23 + 45 + 67 + 89;
a(10) = 237 = -123 + 456 - 7 - 89;
a(11) = 253 = -1 + 2 + 345 - 6 - 78 - 9;
a(12) = 259 = -1 + 234 - 56 - 7 + 89;
a(869) = 123456789 = A136602(1715).

R. Zumkeller, Table of n, a(n) for n = 1..869 (full sequence)

cp's OEIS Frontend

A066957 a(n) = number of ways of placing '+' and '-' among the digits 123456789 so that the result of the expression is n, '-' before 1 IS allowed.

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A136602 Nonnegative numbers that can be obtained by inserting minus and plus-signs in 123456789.

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A136603 Positive numbers having a unique representation by inserting minus and plus-signs in 123456789.

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