A277497 Number of cryptarithms of the form x + y = z in base n for which no summand contains any letter more than once and which have at least one solution.

3, 49, 1020, 28666, 1099824, 57520786, 3882860433, 331811494082

Offset

2,1

Comments

Two cryptarithms are the same if one may be obtained from the other by a process of replacing letters and swapping the summands. For instance, the problem AB + BCD = DDD is the same as ABC + DA = CCC.

Solutions must assign a different digit to each letter, and numbers may not begin with 0.

Links

Table of n, a(n) for n=2..9.

Cryptarithms.com, Cryptarithms - Number Puzzles

Math StackExchange, How many strong simple addition mathagrams of degree one are there in a given base?

Eric M. Schmidt, C++ code to compute this sequence

Eric M. Schmidt, List of solvable problems in base 3

Example

In base 10, the classic SEND + MORE = MONEY has an assignment of digits to the letters that makes the equation true, and is counted because neither SEND nor MORE contains a given letter more than once.
In base 3, CBA + AB = CAA is solvable, and is counted. There are exactly two solutions: (A = 1, B = 0, C = 2) and (A = 2, B = 0, C = 1).

Crossrefs

Cf. A277496.

Sequence in context: A208935 A355882 A202534 * A173174 A302466 A303248

Adjacent sequences: A277494 A277495 A277496 * A277498 A277499 A277500

Keyword

nonn,base,hard,more

Author

Eric M. Schmidt, Oct 18 2016

Status

approved