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A364190
The sum of the digits present in a(n) and a(n+1) divides the product [a(n)*a(n+1)]. This is the lexicographically earliest sequence of distinct positive terms with this property.
0
1, 10, 4, 15, 3, 6, 12, 9, 11, 14, 2, 20, 8, 26, 5, 32, 21, 13, 18, 16, 7, 22, 25, 30, 24, 28, 31, 40, 33, 23, 50, 41, 95, 44, 38, 17, 27, 19, 34, 37, 66, 42, 35, 48, 39, 60, 36, 45, 51, 29, 78, 47, 138, 55, 64, 105, 52, 57, 43, 70, 58, 46, 49, 75, 63, 54, 72, 65, 96, 81, 84, 79
OFFSET
1,2
LINKS
EXAMPLE
digitsum a(1) + digitsum a(2) = 1 + 1 + 0 = 2 and 2 divides 1 * 10 = 10 (result = 5);
digitsum a(2) + digitsum a(3) = 1 + 0 + 4 = 5 and 5 divides 10 * 4 = 40 (result = 8);
digitsum a(3) + digitsum a(4) = 4 + 1 + 5 = 10 and 10 divides 4 * 15 = 60 (result = 6);
digitsum a(4) + digitsum a(5) = 1 + 5 + 3 = 9 and 9 divides 15 * 3 = 45 (result = 5);
digitsum a(5) + digitsum a(6) = 3 + 6 = 9 and 9 divides 3 * 6 = 18 (result = 2); etc.
MATHEMATICA
a[1]=1; a[n_]:=a[n]=(k=1; While[MemberQ[Array[a, n-1], k]||Mod[a[n-1]*k, Total[Join[IntegerDigits@a[n-1], IntegerDigits@k]]]!=0, k++]; k)
Array[a, 60] (* Giorgos Kalogeropoulos, Jul 14 2023 *)
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Eric Angelini, Jul 12 2023
STATUS
approved