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 1-6 of 6 results.

A097371 Numbers n such that n=(d_1+5)(d_2+5)*...*(d_k+5), where d_1 d_2 ... d_k is the decimal expansion of n.

Original entry on oeis.org

50, 210, 450, 780, 1500, 3920, 16500, 91728, 269500, 493920, 1293600, 266378112, 317447424, 1277337600, 14948388000, 48697248600, 379748636467200
Offset: 1

Views

Author

Farideh Firoozbakht, Sep 20 2004

Keywords

Comments

All terms are even.
No other terms below 10^100. - Max Alekseyev, Jan 26 2015

Examples

			317447424 is in the sequence because 317447424=(3+5)(1+5)(7+5)(4+5)(4+5)(7+5)(4+5)(2+5)(4+5).

Crossrefs

Cf. A097372, A098681.

Programs

  • Mathematica
    Do[h=IntegerDigits[n];l=Length[h];If[n==Product[h[[k]]+5, {k, l}], Print[n]], {n, 800000000}]

Extensions

4 more terms from Giovanni Resta, Jan 13 2006

A055482 There exists some k>0 such that n is the product of (k + digits of n).

Original entry on oeis.org

12, 18, 24, 35, 50, 56, 90, 120, 210, 315, 450, 780, 840, 1500, 3920, 4320, 4752, 7744, 16500, 24960, 57915, 59400, 60480, 91728, 269500, 493920, 917280, 1293600, 2419200, 3386880, 34992000, 266378112, 317447424, 1277337600, 3714984000, 14948388000, 48697248600, 460522782720, 896168448000
Offset: 1

Views

Author

Erich Friedman, Jun 27 2000

Keywords

Comments

18 appears to be the only term with k=1, there are no other terms with k=1 as well as with k=3,8,9 below 10^100. - Max Alekseyev, Jan 25 2015

Examples

			4752 = (4+4)(4+7)(4+5)(4+2).

Links

Crossrefs

Cf. A055481, A113756
Subsequences: A098113 (k=2), A098114 (k=4), A097371 (k=5), A097372 (k=6), A115227 (k=7)

Programs

  • Mathematica
    L={}; Do[Print@ n; Do[p = Reverse/@ IntegerPartitions[ k, {n}, Range[0, 9]]; Do[z = Times@@ (e + k); If[ Sort@ IntegerDigits@ z == e, Print[{z, k}]; AppendTo[L, z]], {k, 9}, {e, p}], {k, 9*n}],{n, 2, 13}]; Sort@ L (* terms < 10^13, Giovanni Resta, Jul 24 2015 *)

Extensions

Offset corrected and more terms added by Max Alekseyev, Jan 23 2015

A098113 Numbers n such that n=(d_1+2)*(d_2+2)*...*(d_k+2) where d_1 d_2 ... d_k is the decimal expansion of n.

Original entry on oeis.org

12, 24, 35, 56
Offset: 1

Views

Author

Farideh Firoozbakht, Sep 24 2004

Keywords

Comments

It seems that there are no further terms.
No other terms below 10^150. - Max Alekseyev, Jan 25 2015

Examples

			56 is in the sequence because 56=(5+2)*(6+2).

Crossrefs

Cf. A098114, A097371, A097372.

Programs

  • Mathematica
    Do[d=IntegerDigits[n];k=Length[d];If[n==Product[d[[j]]+2, {j, k}], Print[n]], {n, 10000000}]

A098114 Numbers n such that n=(d_1+4)*(d_2+4)*...*(d_k+4) where d_1 d_2 ... d_k is the decimal expansion of n.

Original entry on oeis.org

120, 315, 4752, 7744, 24960, 57915, 3386880
Offset: 1

Views

Author

Farideh Firoozbakht, Sep 24 2004

Keywords

Comments

Suppose that m is in the sequence and A is set of the digits of m if 6, s times appears in A, then 10^s divides m, also if 1 is in A and at least one even number be in A then 10 divides m, etc.
No other terms below 10^100. - Max Alekseyev, Jan 25 2015

Examples

			3386880 is in the sequence because
3386880=(3+4)*(3+4)*(8+4)*(6+4)*(8+4)*(8+4)*(0+4).

Crossrefs

Cf. A097371, A097372, A098113.

Programs

  • Mathematica
    Do[d=IntegerDigits[n];k=Length[d];If[n==Product[d[[j]]+4, {j, k}], Print[n]], {n, 1030000000}]
Select[Range[4000000],#==Times@@(IntegerDigits[#]+4)&] (* Harvey P. Dale, Dec 11 2012 *)

A115227 Numbers k such that k = (d_1+7)(d_2+7)*...*(d_m+7) where d_1 d_2 ... d_m is the decimal expansion of k.

Original entry on oeis.org

8314460009856000, 31746120037632000, 92632873013093597184000000, 1108240107492643314063114240000, 25425833233403394290952098021376000000000, 67839608823081187608930897100800000000000, 1064102035269050218905833606927320350720000000
Offset: 1

Views

Author

Giovanni Resta, Jan 16 2006

Keywords

Examples

			a(1) = 8314460009856000 = (7+8)*(7+3)*(7+1)*...*(7+6)*(7+0)*(7+0)*(7+0).

Links

Crossrefs

Cf. A055482, A098113, A098114, A097371, A097372, A113756

Extensions

a(6)-a(18) from Max Alekseyev, Jan 25 2015

A113756 Numbers n>9 such that n=Abs[(c+d_1)*(c+d_2)*...*(c+d_k)] where d_1 d_2 ... d_k is the decimal expansion of n and c is an integer constant.

Original entry on oeis.org

12, 18, 24, 35, 50, 56, 90, 100, 120, 180, 210, 315, 350, 450, 500, 672, 728, 780, 840, 910, 1500, 1800, 3150, 3500, 3920, 4320, 4752, 5000, 7056, 7200, 7744, 8960, 16500, 18000, 19008, 24960, 31500, 35000, 50000, 57915, 59400, 60480, 67392, 91728
Offset: 1

Views

Author

Giovanni Resta, Jan 17 2006

Keywords

Comments

Some entries, namely 12, 18, 24, 35, 50, 56, 90, 120, 210, 315, 840, 4752, 7744, 917280 (up to 10^20), have 2 representations, e.g., 840 for c=6 and c=-14 or 917280 for c=6 and c=-15. Sequence is infinite since contains 35*10^k, 315*10^k, 18*10^k and 5*10^k, for k>=0 and c=-10.

Examples

			315 belongs since 315=|(4+3)(4+1)(4+5)|
728 belongs since 728=|(-15+7)(-15+2)(-15+8)|

Crossrefs

Cf. A055482, A115227, A098113, A098114, A097371, A097372.

Programs

  • Mathematica
    L = {}; Do[d = IntegerDigits@n; Do[If[n == Abs[Times @@ (d + c)], AppendTo[L, {n, c}]; Print[{n, c}]], {c, -19, 10}], {n, 10, 1000000}]; Print[Union[Transpose[L][[1]]]]; L
Showing 1-6 of 6 results.

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

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