A352440 Numbers k whose decimal expansion starts with the sum of the last three digits of k.

100, 109, 119, 129, 139, 149, 159, 169, 179, 189, 199, 200, 300, 400, 500, 600, 700, 800, 900, 1001, 1010, 1019, 1028, 1037, 1046, 1055, 1064, 1073, 1082, 1091, 1100, 1119, 1128, 1137, 1146, 1155, 1164, 1173, 1182, 1191, 1219, 1228, 1237, 1246, 1255, 1264, 1273, 1282, 1291, 1319, 1328, 1337, 1346

Offset

1,1

Links

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

Example

   100 is a term because  "100" starts with  "1" = 1 + 0 + 0;
   109 is a term because  "109" starts with "10" = 1 + 0 + 9;
  1346 is a term because "1346" starts with "13" = 3 + 4 + 6; etc.

Mathematica

q[n_] := Module[{d = IntegerDigits[n], s, ds, nds}, s = Plus @@ d[[-3 ;; -1]]; ds = IntegerDigits[s]; nds = Length[ds]; ds == d[[1 ;; nds]]]; Select[Range[100, 1400], q] (* Amiram Eldar, Mar 16 2022 *)
ltd[n_]:=Module[{idn=IntegerDigits[n], t3}, t3=IntegerDigits[Total[Take[idn, -3]]]; Take[idn, Length[t3]]==t3]; Select[Range[100, 1400], ltd] (* Harvey P. Dale, Oct 13 2025 *)

Prog

(Python)
def ok(n):
    s = str(n)
    return n > 99 and s.startswith(str(sum(map(int, s[-3:]))))
print([k for k in range(1347) if ok(k)]) # Michael S. Branicky, Mar 16 2022

Crossrefs

Cf. A352438, A352439.

Sequence in context: A204587 A204588 A369636 * A204589 A134496 A380596

Adjacent sequences: A352437 A352438 A352439 * A352441 A352442 A352443

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, Mar 16 2022

Status

approved