A296451 Anagraprod Integers. Integers N that reproduce their multiset of digits when all the products of two successive digits of N are done (and considered together).

135, 162, 261, 531, 1135, 1162, 1326, 1350, 1620, 2135, 2162, 2610, 2611, 2612, 2613, 2614, 2615, 2616, 2617, 2618, 2619, 3135, 3162, 4135, 4162, 5135, 5162, 5310, 5311, 5312, 5313, 5314, 5315, 5316, 5317, 5318, 5319, 6135, 6162, 6231, 7135, 7162, 8135, 8162, 9135, 9162, 11135, 11162, 11326, 11350, 11620, 13260, 13500, 16200, 21135, 21162, 21326, 21350, 21620, 22134, 23126, 26100, 26110, 26111, 26112, 26113, 26114, 26115

Offset

1,1

Comments

The sequence is infinite as each term can be extended with as many zeros as wanted. The name "anagraprod numbers" comes from "anagram by product". The "anagrasum numbers" are A296521.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..500 (first 304 terms from Georges Brougnard)

Example

135 reproduces the digits 1, 3 and 5 (in a different order) when the products 1*3=3 and 3*5=15 are done. The same with 162 which reproduces the digit 1, 6 and 2 when the products 1*6=6 and 6*2=12 are made.
1135 is a term: 1*1 = 1, 1*3 = 3, 3*5 = 15 -> multiset {1,1,3,5}.
2162 is a term: 2*1 = 2, 1*6 = 6, 6*2 = 12 -> multiset {1,2,2,6}.

Mathematica

A296451Q[k_] := Sort[Flatten[IntegerDigits[Times @@@ Partition[#, 2, 1]]]] == Sort[#] & [IntegerDigits[k]];
Select[Range[10000], A296451Q] (* Paolo Xausa, Nov 30 2024 *)

Prog

(Python)
def ok(n):
    s = str(n)
    d = list(map(int, s))
    sums = [d[i]*d[i+1] for i in range(len(s)-1)]
    return sorted(s) == sorted("".join(str(t) for t in sums))
print([k for k in range(10**5) if ok(k)]) # Michael S. Branicky, Nov 27 2024

Crossrefs

Cf. A296521, A297627.

Sequence in context: A235809 A066176 A025363 * A096593 A050215 A358778

Adjacent sequences: A296448 A296449 A296450 * A296452 A296453 A296454

Keyword

nonn,base

Author

Eric Angelini and Georges Brougnard, Dec 13 2017

Status

approved