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A364275
Lexicographically earliest sequence of distinct positive terms such that the cumulative sum Q(n) of the first n terms of the sequence has at least one duplicated digit.
1
11, 22, 33, 34, 1, 9, 2, 3, 4, 12, 10, 14, 6, 5, 15, 7, 23, 13, 8, 20, 25, 26, 19, 16, 17, 18, 27, 24, 21, 29, 31, 28, 32, 30, 38, 35, 39, 37, 43, 41, 40, 51, 36, 42, 44, 47, 45, 46, 48, 50, 53, 58, 52, 54, 56, 49, 57, 55, 59, 61, 60, 64, 65, 62, 69, 63, 66, 72, 68, 74
OFFSET
1,1
COMMENTS
The sequence is infinite. Does a term a(n) exist such that from a(n) on a(n+1) is always a(n) + 1?
EXAMPLE
a(1) = 11 and Q(1) = 11 (with two 1s);
a(2) = 22 and Q(2) = 33 (with two 3s);
a(3) = 33 and Q(3) = 66 (with two 6s);
a(4) = 34 and Q(4) = 100 (with two 0s);
a(5) = 1 and Q(5) = 101 (with two 1s);
a(6) = 9 and Q(6) = 110 (with two 1s); etc.
MATHEMATICA
a[1]=11; a[n_]:=a[n]=(k=1; While[DuplicateFreeQ@IntegerDigits@ Total[Join[c=Array[a, n-1], {k}]]||MemberQ[c, k], k++]; k); Array[a, 70] (* Giorgos Kalogeropoulos, Jul 19 2023 *)
CROSSREFS
Cf. A364274.
Sequence in context: A178897 A013576 A065998 * A351877 A073729 A073730
KEYWORD
base,nonn
AUTHOR
Eric Angelini, Jul 17 2023
STATUS
approved