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.

A062998 Numbers whose sum of digits is less than or equal to its product of digits.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 22, 23, 24, 25, 26, 27, 28, 29, 32, 33, 34, 35, 36, 37, 38, 39, 42, 43, 44, 45, 46, 47, 48, 49, 52, 53, 54, 55, 56, 57, 58, 59, 62, 63, 64, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 77, 78, 79, 82, 83, 84, 85, 86, 87, 88, 89, 92, 93, 94, 95, 96, 97, 98, 99, 123, 124, 125, 126, 127, 128, 129, 132, 133, 134, 135
Offset: 1

Views

Author

Henry Bottomley, Jun 29 2001

Keywords

Links

Crossrefs

Cf. A007953, A007954, A034710, A062329, A062996, A062997, A062998, A062999.
Not the same as A037344 (contains 124).

Programs

  • Maple
    isA062998 := proc(n)
        local dgs,s,p ;
        dgs := convert(n,base,10) ;
        s := add(i,i=dgs) ;
        p := mul(i,i=dgs) ;
        if s <= p then
                true;
        else
                false;
        end if;
end proc:
for n from 2 to 150 do
        if isA062998(n) then
                printf("%d,",n) ;
        end if;
end do:   # R. J. Mathar, Aug 14 2025
  • Mathematica
    Select[Range[100],Total[IntegerDigits[#]]<=Times@@IntegerDigits[#]&] (* Harvey P. Dale, Feb 21 2017 *)
  • PARI
    isok(k)={my(d=digits(k)); vecsum(d) <= vecprod(d)} \\ Harry J. Smith, Aug 15 2009
  • PARI
    is_A062998(n)={normlp(n=digits(n),1)<=prod(i=1,#n,n[i])} \\ M. F. Hasler, Oct 29 2014

A062996 Numbers whose sum of digits is greater than or equal to its product of digits.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 30, 31, 40, 41, 50, 51, 60, 61, 70, 71, 80, 81, 90, 91, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 130, 131, 132
Offset: 1

Views

Author

Henry Bottomley, Jun 29 2001

Keywords

Links

Crossrefs

Cf. A007953, A007954, A034710, A062329, A062996, A062997, A062998, A062999.

Programs

  • Mathematica
    Select[Range[150],Total[IntegerDigits[#]]>=Times@@IntegerDigits[#]&] (* Harvey P. Dale, Sep 27 2023 *)
  • PARI
    isok(k)={my(d=digits(k)); vecsum(d) >= vecprod(d)} \\ Harry J. Smith, Aug 15 2009

A062329 a(n) = (sum of digits of n) - (product of digits of n).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, 3, 1, -1, -3, -5, -7, -9, -11, -13, -15, 4, 1, -2, -5, -8, -11, -14, -17, -20, -23, 5, 1, -3, -7, -11, -15, -19, -23, -27, -31, 6, 1, -4, -9, -14, -19, -24, -29, -34, -39, 7, 1, -5, -11, -17, -23, -29, -35, -41, -47, 8, 1, -6, -13, -20, -27
Offset: 0

Views

Author

Amarnath Murthy, Jun 21 2001

Keywords

Examples

			a(23) = 2 + 3 - 2*3 = -1.
a(49) = -(4*9) + (4 + 9) = -36 + 13 = -23.

Links

Crossrefs

Cf. A007953, A007954, A034710, A062996, A062997, A062998, A062999, A070565.
A063543 has a similar graph.

Programs

  • Mathematica
    a[n_] := (t = IntegerDigits[n]; Plus @@ t - Times @@ t); Table[ a[n], {n, 0, 75}] (* Robert G. Wilson v *)

Extensions

Corrected and extended by Larry Reeves (larryr(AT)acm.org), Jun 22 2001
Signed version from Henry Bottomley, Jun 29 2001

A062997 Numbers whose sum of digits is strictly greater than its product of digits.

Original entry on oeis.org

10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 30, 31, 40, 41, 50, 51, 60, 61, 70, 71, 80, 81, 90, 91, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 130, 131, 140, 141, 150, 151, 160, 161, 170
Offset: 1

Views

Author

Amarnath Murthy, Jun 27 2001

Keywords

Comments

Every multiple of 10 is a term.

Examples

			118 is a term as 1 + 1 + 8 = 10, 10 > 8 and 8 = 1 * 1 * 8.

Links

Crossrefs

Cf. A007953, A007954, A034710, A062329, A062996, A062998, A062999.

Programs

  • Mathematica
    Select[Range[170], (Plus @@ IntegerDigits[ # ]) > (Times @@ IntegerDigits[ # ]) &] (* Alonso del Arte, May 16 2005 *)
  • PARI
    isok(k)={my(d=digits(k)); vecsum(d) > vecprod(d)} \\ Harry J. Smith, Aug 15 2009

Extensions

Extended by Larry Reeves (larryr(AT)acm.org) and Henry Bottomley, Jun 29 2001

A254621 Zerofree numbers having product of digits less than or equal to sum of digits.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 31, 41, 51, 61, 71, 81, 91, 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 122, 123, 131, 132, 141, 151, 161, 171, 181, 191, 211, 212, 213, 221, 231, 311, 312, 321, 411
Offset: 1

Views

Author

David A. Corneth, Feb 03 2015

Keywords

Comments

Intersection of A052382 and A062996.
The repunit A002275(k), for k >= 2, appears at position A254622(k-1) + 1. - Wolfdieter Lang, Feb 23 2015

Links

Crossrefs

Cf. A052382, A062996, A062997, A062998, A062999, A254622, A002275.

Programs

  • Maple
    extend:= proc(t, b, d)
  local i,j,m,s,p;
  p:= t[2];
  s:= t[3];
  if s = 0  then if b=2 then j:= 3 else j:= 2 fi
  else  for j from 0 to d-nops(t[1]) while p*b^j <= s + j*b do od
  fi:
  seq([[op(t[1]),b$i],p*b^i,s+i*b],i=0..j-1);
end proc:
f:= proc(d)
   local j, b, Res;
   Res:= [seq([[1$j],1,j],j=0..d)];
   for b from 2 to 9 do
     Res:= map(extend,Res,b,d)
   od:
   Res:= map(t -> op(combinat:-permute(t[1])),Res);
   subs(0=NULL,sort(map(t -> add(t[i]*10^(i-1),i=1..nops(t)), Res)));
end proc:
f(5); # Robert Israel, May 19 2015
  • Mathematica
    m[w_] := Flatten@Table[i, {i,9}, {w[[i]]}]; a[upd_] := Union@ Flatten@ Table[ FromDigits /@ Flatten[Permutations /@ m /@ Select[ Flatten[ Permutations /@ (IntegerPartitions[d + 9, {9}, Range[d + 1]] - 1), 1], Times @@ (Range[9]^#) <= Total[# Range[9]] &], 1], {d,  upd}]; a[12] (* terms with up to 12 digits, Giovanni Resta, May 19 2015 *)
zfnQ[n_]:=Module[{idn=IntegerDigits[n]},FreeQ[idn,0]&&Times@@idn <= Total[ idn]]; Select[Range[500],zfnQ] (* Harvey P. Dale, Jun 29 2019 *)
  • PARI
    is(n)={my(d=digits(n));my(p=prod(i=1,#d,d[i])); 0 < p && p<=vecsum(d) } \\ David A. Corneth, May 15 2015
Showing 1-5 of 5 results.

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

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