A352461 Numbers k whose decimal expansion starts with the sum of digits of k.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 109, 119, 129, 139, 149, 159, 169, 179, 189, 199, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1009, 1018, 1027, 1036, 1045, 1054, 1063, 1072, 1081, 1090, 1109, 1118, 1127, 1136, 1145, 1154, 1163, 1172, 1181, 1190, 1209, 1218, 1227, 1236

Offset

1,2

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

    10 is a term because   "10" starts with  "1", which is the sum 1 + 0.
   119 is a term because  "119" starts with "11", which is the sum 1 + 1 + 9.
  1018 is a term because "1018" starts with "10", which is the sum 1 + 0 + 1 + 8.

Mathematica

q[n_] := Module[{d = IntegerDigits[n], s, ds, nds}, s = Plus @@ d; ds = IntegerDigits[s]; nds = Length[ds]; ds == d[[1 ;; nds]]]; Select[Range[1240], q] (* Amiram Eldar, Mar 17 2022 *)
Select[Range[1236], StringStartsQ[ToString[#], ToString[Plus@@IntegerDigits[#]]]&] (* Ivan N. Ianakiev, Mar 18 2022 *)
Select[Range[1300], SequencePosition[IntegerDigits[#], IntegerDigits[Total[IntegerDigits[#]]]][[;; , 1]]=={1}&] (* Harvey P. Dale, Nov 03 2024 *)

Prog

(Python)
def ok(n): s = str(n); return s.startswith(str(sum(map(int, s))))
print([k for k in range(1, 1237) if ok(k)]) # Michael S. Branicky, Mar 17 2022

Crossrefs

Cf. A052018, A352462.

Sequence in context: A032945 A236402 A052018 * A302768 A202272 A180480

Adjacent sequences: A352458 A352459 A352460 * A352462 A352463 A352464

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, Mar 17 2022

Status

approved