A216188 Number of unordered pairs of anagrammatic (positive) integers adding to n.

0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 3, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 3, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0

Offset

1,44

Comments

Two positive integers are here defined as "anagrammatic" if (in base 10) they have the same number of 0 digits, 1 digits, 2 digits, ..., 9 digits. Thus, 123 and 231 are anagrammatic, but not 301 and 013, as leading zeros are omitted.

Links

Christian Schulz, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

Example

For n = 88, the a(88) = 4 pairs are {17,71}, {26,62}, {35,53}, and {44,44}. For n = 609, the a(609) = 1 pair is {237,372}.

Maple

getDigit := (n, k) -> floor(n/10^k) mod 10; getMaxDigit := n -> floor(log10(n)) + 1; getDigitMultiset := n -> convert([seq(getDigit(n, k), k=0..getMaxDigit(n)-1)], multiset); isAnagram := (m, n) -> evalb(getDigitMultiset(m) = getDigitMultiset(n)); A216188 := n -> convert([seq(eval(isAnagram(k, n-k), [true=1, false=0]), k=1..floor(n/2))], `+`); seq(A216188(n), n=1..50)

Mathematica

IsAnagram[x_, y_, b_: 10] := Sort[Permutations[IntegerDigits[x, b]]] == Sort[Permutations[IntegerDigits[y, b]]]; FindAnagramSums[n_, b_: 10] := Select[Table[{k, n - k}, {k, 0, Floor[n/2]}], IsAnagram[#[[1]], #[[2]], b] &]; Table[Length[FindAnagramSums[n]], {n, 1, 200}]

Crossrefs

Sequence in context: A292262 A160804 A085854 * A117145 A338822 A083912

Adjacent sequences: A216185 A216186 A216187 * A216189 A216190 A216191

Keyword

nonn,base

Author

Christian Schulz, Mar 11 2013

Status

approved