A364120 Digitsum of a(n) + digitsum of a(n+1) divides a(n+2). This is the lexicographically earliest sequence of distinct positive terms with this property.

1, 2, 3, 5, 8, 13, 12, 7, 10, 16, 24, 26, 14, 39, 17, 20, 30, 15, 9, 45, 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198, 27, 81, 216, 234, 252, 270, 288, 135, 189, 243, 297, 324, 351, 306, 342, 360, 378, 405, 432, 396, 459, 468, 504, 486, 513, 540, 414, 450, 522, 558, 567, 576, 612, 594, 621, 648, 675, 684

Offset

1,2

Links

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

Eric Angelini, SuperSums, SuperProducts, personal blog.

Michael De Vlieger, Log log scatterplot of a(n), n = 1..2^20.

Example

digitsum a(1) + digitsum a(2) = 1 + 2 = 3 and 3 divides exactly a(3) = 3;
digitsum a(2) + digitsum a(3) = 2 + 3 = 5 and 5 divides exactly a(4) = 5;
digitsum a(3) + digitsum a(4) = 3 + 5 = 8 and 8 divides exactly a(5) = 8;
digitsum a(4) + digitsum a(5) = 5 + 8 = 13 and 13 divides exactly a(6) = 13;
digitsum a(5) + digitsum a(6) = 8 + 1 + 3 = 12 and 12 divides exactly a(7) = 12; etc.

Mathematica

nn = 80; c[_] := False; m[_] := 1; Array[Set[{a[#], c[#]}, {#, True}] &, 2]; d = i = 1; dd = j = 2; Do[k = d + dd; While[c[k m[k]], m[k]++]; k *= m[k]; Set[{a[n], c[k], i, j, d, dd}, {k, True, j, k, dd, Total@ IntegerDigits[k]}], {n, 3, nn}]; Array[a, nn] (* Michael De Vlieger, Jul 12 2023 *)

Prog

(PARI) {a=List(u=[1, 2]); for(n=2, 99, s=sumdigits(a[n-1])+sumdigits(a[n]);
forstep(k=s, oo, s, set search (u, k)&& next; listput(a, k); u=setunion(u, [k]);
break)); a}

Crossrefs

Cf. A007953, A364187, A364188.

Sequence in context: A131297 A267809 A010077 * A065076 A069638 A237568

Adjacent sequences: A364117 A364118 A364119 * A364121 A364122 A364123

Keyword

base,nonn

Author

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

Extensions

Edited definition. - N. J. A. Sloane, Aug 26 2023

Status

approved