A177902 Numbers k such that d(i)|(k - i) for i = 1..p where d(1), d(2), ..., d(p) are the digits of the decimal expansion of k.

1, 11, 12, 14, 18, 21, 23, 29, 31, 34, 37, 41, 51, 56, 61, 71, 81, 91, 111, 131, 157, 191, 211, 213, 219, 437, 511, 857, 1111, 1112, 1117, 1121, 1123, 1129, 1131, 1153, 1161, 1172, 1187, 1191, 1212, 1216, 1512, 1731, 2111, 2113, 2119, 2121, 2143, 2173, 2321, 2517, 2587, 2711, 3112, 3121, 3712, 4121, 4153, 4161, 4197, 5111, 5116, 5121, 5176, 5321, 5721, 6121, 7512, 8113, 8121, 8321, 8921

Offset

1,2

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..500 from Harvey P. Dale)

Example

925678 is in the sequence because
  9 | 925677,
  2 | 925676,
  5 | 925675,
  6 | 925674,
  7 | 925673,
  8 | 925672.

Maple

with(numtheory):for n from 1 to 10000 do:i:=0:l:=length(n):n0:=n:s:=0:for m
  from 0 to l-1 do:q:=n0:u:=irem(q, 10):v:=iquo(q, 10):n0:=v :w:=n-l+m:if u<>0 and
  irem(w, u)=0 then i:=i+1:else fi:od:if i=l then printf(`%d, `, n):else fi:od:

Mathematica

okQ[n_]:=Module[{idn=IntegerDigits[n]}, !MemberQ[idn, 0]&&And@@Divisible[ Table[n-i, {i, Length[idn]}], Table[idn[[j]], {j, Length[idn]}]]]; Select[ Range[ 9000], okQ] (* Harvey P. Dale, Sep 25 2011 *)

Prog

(Sage) is_A177902 = lambda n: all(d.divides(n-i) for i, d in enumerate(n.digits()[::-1], 1)) # D. S. McNeil, Dec 16 2010
(Python)
def ok(n): return all(di!=0 and (n-i)%di==0 for i, di in enumerate(map(int, str(n)), 1))
print([k for k in range(9000) if ok(k)]) # Michael S. Branicky, Feb 20 2023
(Python) # faster version for b-file/initial segment of sequence
from itertools import count, islice, product
def agen():
    for digits in count(1):
        for d in product("123456789", repeat=digits):
            k = int("".join(d))
            if all((k-i)%di==0 for i, di in enumerate(map(int, d), 1)):
                yield k
print(list(islice(agen(), 50))) # Michael S. Branicky, Feb 20 2023

Crossrefs

Sequence in context: A182404 A234021 A264023 * A108722 A246139 A034907

Adjacent sequences: A177899 A177900 A177901 * A177903 A177904 A177905

Keyword

nonn,base

Author

Michel Lagneau, Dec 15 2010

Status

approved