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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.
5
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
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
KEYWORD
base,nonn
AUTHOR
Eric Angelini and M. F. Hasler, Jul 12 2023
STATUS
approved