A352461 -id:A352461 - cp's OEIS frontend

A352462 Numbers k with the property that k ends in the sum of the digits of k.

1, 2, 3, 4, 5, 6, 7, 8, 9, 910, 911, 912, 913, 914, 915, 916, 917, 918, 919, 1810, 1811, 1812, 1813, 1814, 1815, 1816, 1817, 1818, 1819, 2710, 2711, 2712, 2713, 2714, 2715, 2716, 2717, 2718, 2719, 3610, 3611, 3612, 3613, 3614, 3615, 3616, 3617, 3618, 3619, 4510, 4511, 4512, 4513, 4514, 4515, 4516

Offset: 1

Eric Angelini and Carole Dubois, Mar 17 2022

			a(10) = 910, which ends in 10 = 9 + 1 + 0.
a(20) = 1810, which ends in 10 = 1 + 8 + 1 + 0.
a(39) = 2719, which ends in 19 = 2 + 7 + 1 + 9.

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

Cf. A052018, A352461.

q[n_] := Module[{d = IntegerDigits[n], s, ds, nds}, s = Plus @@ d; s = IntegerDigits[s]; nds = Length[ds]; ds == d[[-nds ;; -1]]]; Select[Range[4516], q] (* Amiram Eldar, Mar 17 2022 *)
Select[Range[4516],StringEndsQ[ToString[#],ToString[Plus@@IntegerDigits[#]]]&] (* Ivan N. Ianakiev, Mar 18 2022 *)
sdkQ[n_]:=Module[{idn=IntegerDigits[n],d},d=IntegerDigits[Total[idn]];d==Take[idn,-Length[d]]]; Select[Range[5000],sdkQ] (* Harvey P. Dale, Apr 19 2022 *)

def ok(n): s = str(n); return s.endswith(str(sum(map(int, s))))
print([k for k in range(1, 4517) if ok(k)]) # Michael S. Branicky, Mar 17 2022

A352463 Numbers k with the property that the product of the digits of k starts k.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 21, 31, 41, 51, 61, 71, 81, 91, 111, 126, 153, 211, 243, 311, 362, 411, 511, 611, 711, 811, 911, 1111, 1216, 1223, 1232, 1261, 1288, 1359, 1449, 1513, 1531, 1755, 2111, 2413, 2431, 3111, 3612, 3621, 3844, 4111, 5111, 6111, 6728, 7111, 7357, 8111, 9111, 11111, 11278, 11287

Offset: 1

Eric Angelini and Carole Dubois, Mar 17 2022

			a(10) = 11 starts with 1, which is the product 1*1;
a(20) = 126 starts with 12, which is the product 1*2*6;
a(42) = 1755 starts with 175, which is the product ; 1*7*5*5; etc.

Cf. A203565, A352461, A352464.

q[n_] := Module[{d = IntegerDigits[n], p, dp, ndp}, p = Times @@ d; dp = IntegerDigits[p]; ndp = Length[dp]; dp == d[[1 ;; ndp]]]; Select[Range[12000], q] (* Amiram Eldar, Mar 18 2022 *)

from math import prod
def ok(n): s = str(n); return s.startswith(str(prod(map(int, s))))
print([k for k in range(1, 12000) if ok(k)]) # Michael S. Branicky, Mar 17 2022

cp's OEIS Frontend

A352462 Numbers k with the property that k ends in the sum of the digits of k.

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