cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A230099 a(n) = n + (product of digits of n).

Original entry on oeis.org

0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 30, 34, 38, 42, 46, 50, 54, 58, 62, 66, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 50, 56, 62, 68, 74, 80, 86, 92, 98, 104, 60, 67, 74, 81, 88, 95, 102, 109, 116, 123, 70, 78, 86, 94, 102, 110, 118, 126
Offset: 0

Views

Author

N. J. A. Sloane, Oct 12 2013

Keywords

Comments

A230099, A063114, A098736, A230101 are analogs of A092391 and A062028.

Links

Crossrefs

Cf. A007954, A011540, A092391, A062028, A004207, A230093, A003052, A176995.
Cf. also A063114, A098736, A230101, A230103, A230104, A230105, A062028, A230102, A063108.

Programs

  • Haskell
    a230099 n = a007954 n + n  -- Reinhard Zumkeller, Oct 13 2013
  • Maple
    with transforms; [seq(n+digprod(n), n=0..200)];
  • PARI
    a(n) = if (n, n + vecprod(digits(n)), 0); \\ Michel Marcus, Dec 18 2018
  • Python
    from math import prod
def a(n): return n + prod(map(int, str(n)))
print([a(n) for n in range(78)]) # Michael S. Branicky, Jan 09 2023

Formula

a(n) = n iff n contains a digit 0 (A011540). - Bernard Schott, Jul 31 2023

A230103 Number of m such that m + (product of digits of m) equals n.

Original entry on oeis.org

1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 2, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 3, 0, 0, 0, 1, 1, 1, 0, 1, 0, 2, 0, 2, 0, 0, 1, 1, 1, 1, 0, 2, 0, 0, 0, 2, 1, 0, 0, 1, 0, 3, 1, 0, 0, 0, 1, 2, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 2, 0, 2, 1, 3
Offset: 0

Views

Author

N. J. A. Sloane, Oct 13 2013

Keywords

Comments

Number of times n appears in A230099.

Links

Crossrefs

Cf. A230099, A230104.

Programs

  • Maple
    # Maple code for A230099, A230103, A230104, A230105
with(LinearAlgebra):
read transforms; # to get digprod
M:=1000;
lis1:=Array(0..M);
lis2:=Array(0..M);
ctmax:=4;
for i from 0 to ctmax do ct[i]:=Array(0..M); od:
for n from 0 to M do
m:=n+digprod(n);
lis1[n]:=m;
if (m <= M) then lis2[m]:=lis2[m]+1; fi;
od:
t1:=[seq(lis1[i],i=0..M)]; # A230099
t2:=[seq(lis2[i],i=0..M)]; # A230103
COMPl(t1); # A230104
for i from 1 to M do h:=lis2[i];
if h <= ctmax then ct[h]:=[op(ct[h]),i]; fi; od:
len:=nops(ct[0]); [seq(ct[0][i],i=1..len)]; # A230104 again
len:=nops(ct[1]); [seq(ct[1][i],i=1..len)]; # A230105
  • PARI
    a(n) = if (n==0, return(1)); sum(k=1, n, k+vecprod(digits(k)) == n); \\ Michel Marcus, Sep 18 2020
  • Python
    from math import prod
def b(n): return n + prod(map(int, str(n)))
def a(n): return sum(1 for m in range(n+1) if b(m) == n)
print([a(n) for n in range(103)]) # Michael S. Branicky, Jan 09 2023
  • Python
    # faster version for initial segment of sequence
from math import prod
from collections import Counter
def b(n): return n + prod(map(int, str(n)))
def aupto(n):
    c = Counter(b(m) for m in range(n+1))
    return [c[k] for k in range(n+1)]
print(aupto(102)) # Michael S. Branicky, Jan 09 2023

A230105 Numbers n such that m + (product of digits of m) = n has exactly one solution m.

Original entry on oeis.org

0, 2, 4, 6, 8, 22, 23, 24, 28, 29, 30, 32, 34, 35, 40, 41, 42, 44, 45, 46, 47, 54, 55, 56, 58, 65, 66, 67, 68, 75, 78, 81, 85, 88, 89, 90, 92, 94, 95, 101, 103, 105, 106, 108, 112, 114, 122, 124, 125, 128, 129, 132, 135, 141, 143, 144, 145, 146, 147, 152, 154, 155, 156, 158, 161, 165, 166, 167, 168, 175, 178, 181, 185
Offset: 1

Views

Author

N. J. A. Sloane, Oct 13 2013

Keywords

Comments

Numbers n such that A230103(n) = 1.

Links

Crossrefs

Cf. A230099, A230103, A230104.

Programs

  • Python
    from math import prod
from collections import Counter
def b(n): return n + prod(map(int, str(n)))
def aupto(n):
    c = Counter(b(m) for m in range(n+1))
    return [k for k in range(n+1) if c[k] == 1]
print(aupto(185)) # Michael S. Branicky, Jan 09 2023

A230106 Number of m such that m + (product of nonzero digits of m) equals n.

Original entry on oeis.org

0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 2, 0, 2, 0, 2, 0, 2, 0, 1, 0, 2, 1, 1, 0, 2, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 2, 0, 0, 1, 1, 0, 2, 1, 1, 1, 0, 0, 2, 0, 0, 0, 1, 2, 1, 0, 1, 0, 1, 0, 2, 0, 0, 1, 2, 1, 1, 0, 1, 0, 0, 0, 2, 1, 0, 1, 1, 0, 2, 1, 0, 0, 0, 1, 2, 0, 2, 1, 0, 0, 1, 0, 1, 1, 0, 0, 2, 1, 1, 1, 3
Offset: 0

Views

Author

N. J. A. Sloane, Oct 13 2013

Keywords

Comments

Number of times n appears in A063114.

Links

Crossrefs

Cf. A063108, A063114, A230099, A230104, A063425, A096922.
Variant of A096972.

Programs

  • Maple
    # Maple code for A063114, A230106, A063425, A096922
with(LinearAlgebra):
read transforms; # to get digprod0
M:=1000;
lis1:=Array(0..M);
lis2:=Array(0..M);
ctmax:=4;
for i from 0 to ctmax do ct[i]:=Array(0..M); od:
for n from 0 to M do
m:=n+digprod0(n);
lis1[n]:=m;
if (m <= M) then lis2[m]:=lis2[m]+1; fi;
od:
t1:=[seq(lis1[i],i=0..M)]; # A063114
t2:=[seq(lis2[i],i=0..M)]; # A230106
COMPl(t1); # A063425
for i from 1 to M do h:=lis2[i];
if h <= ctmax then ct[h]:=[op(ct[h]),i]; fi; od:
len:=nops(ct[0]); [seq(ct[0][i],i=1..len)]; # A063425 again
len:=nops(ct[1]); [seq(ct[1][i],i=1..len)]; # A096922

Extensions

a(1) corrected by Zak Seidov, Oct 24 2013

A358353 Numbers that are not of the form m + (sum of digits of m) + (product of digits of m) for any m.

Original entry on oeis.org

1, 2, 4, 5, 7, 8, 10, 13, 16, 19, 25, 28, 31, 36, 37, 39, 40, 41, 45, 47, 49, 51, 52, 57, 59, 60, 61, 64, 65, 67, 70, 71, 72, 75, 79, 81, 84, 85, 87, 89, 91, 93, 94, 96, 100, 102, 116, 120, 125, 126, 129, 137, 141, 142, 146, 150, 152, 153, 160, 161, 162, 166, 171, 172, 173, 180
Offset: 1

Views

Author

Bernard Schott, Dec 19 2022

Keywords

Comments

Numbers missing from A358350.
The first differences show some periodicity, for example those for values 2184-3811 repeat at terms 5513-7140. - Bill McEachen, Jan 08 2023

Examples

			There is no term du_10 < 36 such that du + (d+u) + (d*u) = 36, so 36 is a term.

Links

Crossrefs

Cf. A161351, A358350, A358351, A358352.
Similar: A003052 (m+digitsum), A230104 (m+digitprod).

Programs

  • Maple
    f:= proc(n) local L; L:= convert(n,base,10); n + convert(L,`+`)+convert(L,`*`) end proc:
sort(convert({$1..200} minus map(f, {$1..200}),list)); # Robert Israel, Dec 22 2022
  • Mathematica
    f[n_] := n + Total[(d = IntegerDigits[n])] + Times @@ d; With[{m = 180}, Complement[Range[m], Table[f[n], {n, 1, m}]]] (* Amiram Eldar, Dec 19 2022 *)
  • PARI
    f(n) = my(d=digits(n)); vecsum(d)+vecprod(d)+n; \\ A161351
isok(m) = for(i=1, m, if (f(i) == m, return(0))); return(1); \\ Michel Marcus, Jan 09 2023
  • Python
    from math import prod
def sp(n): d = list(map(int, str(n))); return sum(d) + prod(d)
def ok(n): return all(m + sp(m) != n for m in range(n+1))
print([k for k in range(181) if ok(k)]) # Michael S. Branicky, Dec 19 2022
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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