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A370675
Number of unordered pairs of n-digit numbers k1, k2 such that their product has the same multiset of digits as in both k1 and k2 together.
5
0, 7, 156, 3399, 112025, 4505706, 213002162
OFFSET
1,2
COMMENTS
Since multiplication and multiset union are commutative operations, we count unordered pairs, i.e. we can assume that k1 <= k2.
The sequence is nondecreasing, since for any x,y,p such that x*y=p, x0*y0=p00.
The numbers up to n=7 were verified by at least two independent implementations.
The property of possible residues mod 3 and mod 9 for A370676 also holds for this sequence.
EXAMPLE
For n=2 the a(2)=7 solutions are:
15 * 93 = 1395
21 * 60 = 1260
21 * 87 = 1827
27 * 81 = 2187
30 * 51 = 1530
35 * 41 = 1435
80 * 86 = 6880
PROG
(PARI) a370675(n) = {my (np=0, n1=10^(n-1), n2=10*n1-1); for (k1=n1, n2, my(s1=digits(k1)); for (k2=k1, n2, my (s2=digits(k2)); my(sp=digits(k1*k2)); if (#s1+#s2==#sp && vecsort(concat(s1, s2)) == vecsort(sp), np++))); np} \\ Hugo Pfoertner, Feb 26 2024
CROSSREFS
Cf. A114258, A370676 (number of such pairs with possibly unequal number of digits).
Sequence in context: A220367 A220311 A218449 * A197595 A197979 A203584
KEYWORD
nonn,base,more
AUTHOR
Danila Potapov, Feb 26 2024
STATUS
approved