A364187 The sum of the digits present in a(n) and a(n+1) exactly divides the sum [a(n) + a(n+1)]. This is the lexicographically earliest sequence of distinct positive terms with this property.

1, 2, 3, 4, 5, 6, 7, 8, 9, 27, 21, 15, 12, 24, 30, 10, 11, 13, 14, 22, 20, 16, 32, 28, 26, 34, 38, 46, 44, 40, 23, 25, 29, 31, 17, 19, 35, 37, 47, 43, 41, 49, 59, 76, 50, 55, 53, 52, 56, 70, 60

Offset

1,2

Comments

This sequence is most certainly a permutation of the positive integers.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Eric Angelini, SuperSums, SuperProducts, personal blog.

Example

digitsum a(8) + digitsum a(9) = 8 + 9 = 17 and 17 divides exactly a(8) + a(9) = 8 + 9 = 17;
digitsum a(9) + digitsum a(10) = 9 + 2 + 7 = 18 and 18 divides exactly a(9) + a(10) = 9 + 27 = 36;
digitsum a(10) + digitsum a(11) = 2 + 7 + 2 + 1 = 12 and 12 divides exactly a(10) + a(11) = 27 + 21 = 48; etc.

Mathematica

nn = 120; c[_] := False; Array[Set[{a[#], c[#]}, {#, True}] &, 2]; d = j = 2; u = 3; Do[k = u; While[Or[c[k], ! Divisible[j + k, d + Total@ IntegerDigits[k]]], k++]; Set[{a[n], c[k], j, d}, {k, True, k, Total@ IntegerDigits[k]}], {n, 3, nn}]; Array[a, nn] (* Michael De Vlieger, Jul 12 2023 *)

Prog

(PARI) {first(N, U=[], 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), k=U[1]); while(setsearch(U, k++) || (k+a)%(sumdigits(k)+s), ); k, 1))}

Crossrefs

Cf. A007953, A364120, A364188.

Sequence in context: A085123 A131571 A179988 * A179979 A256005 A031309

Adjacent sequences: A364184 A364185 A364186 * A364188 A364189 A364190

Keyword

base,nonn

Author

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

Status

approved