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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.
0
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.
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
KEYWORD
nonn,base
AUTHOR
STATUS
approved