A364188 The sum of the digits present in a(n) and a(n+1) divides exactly the product of the same digits. This is the lexicographically earliest sequence of distinct positive terms with this property.

1, 10, 2, 13, 8, 19, 5, 14, 12, 3, 6, 17, 20, 4, 15, 9, 18, 16, 7, 25, 21, 30, 11, 24, 28, 33, 40, 22, 26, 31, 23, 27, 32, 34, 29, 37, 38, 41, 43, 35, 44, 50, 36, 45, 47, 46, 42, 39, 48, 53, 52, 49, 56, 54, 60, 51, 63, 57, 58, 61, 65, 59, 64, 55, 68, 70, 62, 67, 69, 66, 72, 80, 71, 76, 74, 73, 83, 79, 84

Offset

1,2

Links

Table of n, a(n) for n=1..79.

Eric Angelini, SuperSums, SuperProducts, personal blog.

Example

digitsum a(1) + digitsum a(2) = 1 + 1 + 0 = 2 and 2 divides exactly 1 * 1 * 0 = 0;
digitsum a(2) + digitsum a(3) = 1 + 0 + 2 = 3 and 3 divides exactly 1 * 0 * 2 = 0;
digitsum a(3) + digitsum a(4) = 2 + 1 + 3 = 6 and 6 divides exactly 2 * 1 * 3 = 6;
digitsum a(4) + digitsum a(5) = 1 + 3 + 8 = 12 and 12 divides exactly 1 * 3 * 8 = 24; etc.

Prog

(PARI) {first(N, U=[], P(x)=vecprod(digits(x)), a)=vector(N, n, a=if(n>1, U=setunion(U, [a]); while(#U>1&&U[1]+1==U[2], U=U[^1]); my(s=sumdigits(a), p=P(a), k=U[1]); while(setsearch(U, k++) || P(k)*p%(sumdigits(k)+s), ); k, 1))}

Crossrefs

Cf. A007953, A364187, A364120.

Sequence in context: A069532 A084461 A367811 * A326107 A005483 A228276

Adjacent sequences: A364185 A364186 A364187 * A364189 A364190 A364191

Keyword

nonn

Author

Eric Angelini and M. F. Hasler, Jul 12 2023

Status

approved