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 1-4 of 4 results.

A066282 Numbers k such that k = (product of nonzero digits of k) * (sum of digits of k).

Original entry on oeis.org

0, 1, 135, 144, 1088
Offset: 1

Views

Author

Klaus Brockhaus, Dec 13 2001

Keywords

Comments

Suppose a term k has d digits, then k > 10^(d-1), the product of nonzero digits <= 9^d, and the sum of digits <= 9*d. Since for d >= 85 we have 10^(d-1) > 9^d * (9*d), it follows that d <= 84. That is, the sequence is finite. I've further verified that there are no other terms, that is, the sequence is complete. - Max Alekseyev, Jul 29 2024

Examples

			(1+0+8+8) * (1*8*8) = 17*64 = 1088, so 1088 belongs to the sequence.
		

Crossrefs

Fixed points of A062331.

Programs

  • ARIBAS
    function a066282(a,b: integer); var n,k,j,p,d: integer; s: string; begin for n := a to b do s := itoa(n); k := 0; p := 1; for j := 0 to length(s) - 1 do d := atoi(s[j..j]); k := k + d; if d > 0 then p := p*d; end; end; if n = p*k then write(n,","); end; end; end; a066282(0,25000).
    
  • Mathematica
    Do[ d = Sort[ IntegerDigits[n]]; While[ First[d] == 0, d = Drop[d, 1]]; If[n == Apply[ Plus, d] Apply[ Times, d], Print[n]], {n, 0, 5*10^7} ]
  • PARI
    a066282(a,b) = local(n,k,q,p,d); for(n=a,b,k=0; p=1; q=n; while(q>0,d=divrem(q,10); q=d[1]; k=k+d[2]; p=p*max(1,d[2])); if(n==p*k,print1(n,", ")))
    a066282(0,25000)

Extensions

Offset corrected by Mohammed Yaseen, Jul 21 2022
Keywords fini,full added by Max Alekseyev, Jul 29 2024

A366832 Numbers k such that k = (product of nonzero digits) * (sum of digits) for the digits of k in base 9.

Original entry on oeis.org

1, 12, 1536, 172032, 430080, 4014080
Offset: 1

Views

Author

René-Louis Clerc, Jan 10 2024

Keywords

Comments

There is a finite number of such numbers (Property 1' of Clerc).

Examples

			430080 = 724856_9, (7+2+4+8+5+6)*(7*2*4*8*5*6) = 32*13440 = 430080.
		

Crossrefs

Programs

  • Mathematica
    Select[Range[5*10^6],Total[IntegerDigits[#,9]]*Fold[Times,1,IntegerDigits[#,9]]==#&] (* James C. McMahon, Jan 30 2024 *)
  • PARI
    isok(k, b) = my(d=select(x->(x>0), digits(k,b))); vecprod(d)*vecsum(d) == k;
     for (k=1, 10^7, if (isok(k, 9), print1(k, ", ")))

A367070 Numbers k such that k = (product of nonzero digits) * (sum of digits) for the digits of k in base 7.

Original entry on oeis.org

1, 16, 128, 250, 480, 864, 21600, 62208, 73728
Offset: 1

Views

Author

René-Louis Clerc, Jan 10 2024

Keywords

Comments

There is a finite number of such numbers; we only calculated the terms in [1, 10^10] (Property 1' of Clerc).

Examples

			21600 = 116655_7, (1+1+6+6+5+5)*(1*1*6*6*5*5) = 24*900 = 21600.
		

Crossrefs

Programs

  • Mathematica
    Select[Range[7^7], #1 == Times @@ DeleteCases[#2, 0]*Total[#2] & @@ {#, IntegerDigits[#, 7]} &] (* Michael De Vlieger, Mar 25 2024 *)
  • PARI
    isok(k, b) = my(d=select(x->(x>0), digits(k,b))); vecprod(d)*vecsum(d) == k;
    for (k=1, 10^5, if (isok(k, 7), print1(k, ", ")))

A370251 Base-12 numbers k such that k = (product of nonzero digits of k) * (sum of digits of k) (written in base 10).

Original entry on oeis.org

1, 176, 231, 495, 7040
Offset: 1

Views

Author

René-Louis Clerc, Feb 13 2024

Keywords

Comments

There are only finitely many such numbers (Property 1' of Clerc).

Examples

			231 = 173_12, (1*7*3)*(1+7+3) = 21*11 = 231.
		

Crossrefs

Programs

  • Mathematica
    Select[Range[5*10^4], Total[IntegerDigits[#, 12]]*Fold[Times, 1, Select[IntegerDigits[#, 12],#>0&]]==#&] (* James C. McMahon, Feb 14 2024 *)
  • PARI
    isok(k, b) = my(d=select(x->(x>0), digits(k, b))); vecprod(d)*vecsum(d) == k;
    for (k=0, 10^10, if (isok(k, 12), print1(k, ", ")))
Showing 1-4 of 4 results.