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.

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

Table of n, a(n) for n=1..72.

Eric Angelini, SuperSums, SuperProducts, personal blog.

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

Cf. A007953, A364120, A364187, A364188.

Sequence in context: A076587 A266999 A166204 * A329649 A040094 A094580

Adjacent sequences: A364187 A364188 A364189 * A364191 A364192 A364193

Keyword

base,nonn

Author

Eric Angelini, Jul 12 2023

Status

approved