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A352440
Numbers k whose decimal expansion starts with the sum of the last three digits of k.
1
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
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 *)
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
Sequence in context: A204587 A204588 A369636 * A204589 A134496 A191752
KEYWORD
base,nonn
AUTHOR
Eric Angelini and Carole Dubois, Mar 16 2022
STATUS
approved