A068520 Numbers n which can be transformed into a true arithmetic statement by inserting zero or more parentheses and elementary arithmetic operators ((, ), +, -, *, /) and one equality sign (=) as the rightmost insertion into the decimal representation of n.

11, 22, 33, 44, 55, 66, 77, 88, 99, 100, 101, 110, 111, 112, 122, 123, 133, 134, 144, 145, 155, 156, 166, 167, 177, 178, 188, 189, 199, 200, 202, 211, 212, 213, 220, 221, 224, 235, 236, 246, 248, 257, 268, 279, 300, 303, 312, 313, 314, 321, 325, 326, 330, 331

Offset

1,1

Comments

The minus sign is considered only as two-place infix operator, not as one-place prefix operator. Therefore -1 + 2 = 1 is not allowed and 121 is not a term.

These numbers are called (elementary) "didactic numbers".

Links

Table of n, a(n) for n=1..54.

Sean A. Irvine, Java program (github)

Index entries for similar sequences

Example

7 = 7; 1 * 0 = 0; 2 - 2 = 0; 2 / 2 = 1; 18 / 2 = 9; 2 * (3 + 4) = 14. Therefore 77, 100, 220, 221, 1829 and 23414 are terms of the sequence.
2 - 1 = 1, therefore 211 is a term of the sequence. - Sean A. Irvine, Feb 21 2024

Crossrefs

Sequence in context: A337240 A109303 A338214 * A171901 A033283 A044851

Adjacent sequences: A068517 A068518 A068519 * A068521 A068522 A068523

Keyword

base,nonn

Author

Joseph L. Pe, Mar 21 2002

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Jun 21 2002

Edited by Klaus Brockhaus, Jul 02 2003

Missing 211 inserted by Sean A. Irvine, Feb 21 2024

Status

approved