A371703 Lexicographically earliest sequence of distinct positive terms such that a(n)+a(n+1) and a(n)*a(n+1) have the same set of distinct digits.

1, 100, 10, 898, 134, 398, 33, 669, 83, 1221, 101, 21, 111, 11, 112, 102, 447, 131, 458, 1008, 924, 339, 979, 566, 57, 108, 109, 326, 2247, 1502, 5, 577, 337, 1203, 557, 1692, 4992, 1923, 1749, 41, 1000, 12, 62, 362, 901, 493, 1604, 2500, 105, 49, 169, 1048, 744, 38, 3, 24, 88, 884, 160, 344, 698, 34, 213, 1076, 212, 174

Offset

1,2

Comments

The decimal representation of the sum and the product of any 2 successive terms has the same set of distinct digits.

Links

Table of n, a(n) for n=1..66.

Example

a(8) = 669, then a(9) = 83 because 83 is the least positive integer not appearing in the sequence such that 83 + 669 = 752 and 83 * 669 = 55527 have the same set of distinct digits {2, 5, 7}.

Mathematica

a[1]=1; a[n_]:=a[n]=(k=1; While[MemberQ[Array[a, n-1], k]||Union@IntegerDigits[a[n-1]+k]!=Union@IntegerDigits[a[n-1]*k], k++]; k); Array[a, 70]

Prog

(Python)
from itertools import count, islice
def agen(): # generator of terms
    an, aset = 1, {1}
    while True:
        yield an
        an = next(k for k in count(2) if k not in aset and set(str(an+k)) == set(str(an*k)))
        aset.add(an)
print(list(islice(agen(), 66))) # Michael S. Branicky, Apr 03 2024

Crossrefs

Sequence in context: A273479 A333399 A069037 * A266068 A285648 A084484

Adjacent sequences: A371700 A371701 A371702 * A371704 A371705 A371706

Keyword

nonn,base

Author

Giorgos Kalogeropoulos, Apr 03 2024

Status

approved