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.

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A138961 a(n) = largest prime divisor of A138957(n).

Original entry on oeis.org

1, 3, 41, 617, 823, 643, 9721, 14593, 3803, 14405693, 10939223, 4156374407, 2663693, 5603770631, 1221751714624799, 287108811653770498027, 74103167823547, 11843077531813991, 726216405947772436185983423, 769725127, 18274551225153265813469
Offset: 1

Views

Author

Artur Jasinski, Apr 04 2008

Keywords

Comments

For smallest prime divisors see A138960.

Links

Crossrefs

Cf. A104759, A000422, A116504, A007908, A116505, A104759, A138789, A138790, A138960.

Programs

  • Mathematica
    a = {}; b = {}; Do[w = RealDigits[n]; w = First[w]; Do[AppendTo[a, w[[Length[w] - k + 1]]], {k, 1, Length[w]}]; p = FromDigits[a]; AppendTo[b, First[Last[FactorInteger[p]]]], {n, 1, 18}]; b
A137957[n_] := FromDigits[Flatten[Reverse /@ IntegerDigits[Range[n]]]];
Table[First[Last[FactorInteger[A137957[n]]]], {n, 39}] (* Robert Price, May 10 2019 *)

A138962 a(1) = 1, a(n) = the smallest prime divisor of A138793(n).

Original entry on oeis.org

1, 3, 3, 29, 3, 3, 19, 3, 3, 457, 3, 3, 16087, 3, 3, 35963, 3, 3, 167, 3, 3, 7, 3, 3, 13, 3, 3, 953, 3, 3, 7, 3, 3, 548636579, 3, 3, 19, 3, 3, 71, 3, 3, 13, 3, 3, 89, 3, 3, 114689, 3, 3, 17, 3, 3, 12037, 3, 3, 7, 3, 3
Offset: 1

Views

Author

Artur Jasinski, Apr 04 2008

Keywords

Comments

a(61) > 10^11. - Robert Price, Mar 22 2015

Links

Crossrefs

Cf. A020639, A138793, A104759, A000422, A116504, A007908, A116505, A104759, A075019, A075020, A075021, A075022, A138789, A138790, A138960, A138962.

Programs

  • Mathematica
    b = {}; a = {}; Do[w = RealDigits[n]; w = First[w]; Do[AppendTo[a, w[[k]]], {k, 1, Length[w]}]; p = FromDigits[Reverse[a]]; AppendTo[b, First[First[FactorInteger[p]]]], {n, 1, 31}]; b (* Artur Jasinski, Apr 04 2008 *)
lst = {}; Table[First[First[FactorInteger[FromDigits[Reverse[lst = Join[lst,IntegerDigits[n]]]]]]], {n, 1, 60}] (* Robert Price, Mar 22 2015 *)
  • PARI
    f(n) = my(D = Vec(concat(apply(s->Str(s), [1..n])))); eval(concat(vector(#D, k, D[#D-k+1]))); \\ A138793
a(n) = my(k=f(n)); forprime(p=2, 10^6, if(k%p == 0, return(p))); if(n == 1, 1, vecmin(factor(k)[,1])); \\ Daniel Suteu, May 27 2022

Formula

a(n) = A020639(A138793(n)). - Daniel Suteu, May 27 2022

Extensions

a(32)-a(60) from Robert Price, Mar 22 2015

A138794 a(n) = A138793(n+1)-A138793(n).

Original entry on oeis.org

20, 300, 4000, 50000, 600000, 7000000, 80000000, 900000000, 1000000000, 1100000000000, 210000000000000, 31000000000000000, 4100000000000000000, 510000000000000000000, 61000000000000000000000
Offset: 1

Views

Author

Artur Jasinski, Mar 30 2008

Keywords

Comments

First differences of A138793

Crossrefs

Cf. A000422, A116504, A007908, A116505, A104759, A138789, A138790, A138793, A075019, A075020, A075021, A075022.

Programs

  • Mathematica
    b = {}; a = {}; Do[w = RealDigits[n]; w = First[w]; Do[AppendTo[a, w[[k]]], {k, 1, Length[w]}]; p = FromDigits[Reverse[a]]; AppendTo[b, p], {n, 1, 31}]; c = {}; Do[AppendTo[c, b[[n + 1]] - b[[n]]], {n, 1, Length[b] - 1}]; c (*Artur Jasinski*)

Formula

a(n) = A138793(n+1)-A138793(n)

A138963 a(1) = 1, a(n) = the largest prime divisor of A138793(n).

Original entry on oeis.org

1, 7, 107, 149, 953, 218107, 402859, 4877, 379721, 4349353, 169373, 182473, 1940144339383, 2184641, 437064932281, 5136696159619, 67580875919190833, 1156764458711, 464994193118899, 4617931439293, 1277512103328491957510030561, 8177269604099
Offset: 1

Views

Author

Artur Jasinski, Apr 04 2008

Keywords

Comments

For the smallest prime divisors of A138793 see A138962.

Links

Crossrefs

Cf. A006530, A138793, A138962.
Cf. A104759, A000422, A116504, A007908, A116505, A104759, A075019, A075020, A075021, A075022, A138789, A138790, A138958, A138959, A138960.

Programs

  • Mathematica
    b = {}; a = {}; Do[w = RealDigits[n]; w = First[w]; Do[AppendTo[a, w[[k]]], {k, 1, Length[w]}]; p = FromDigits[Reverse[a]]; AppendTo[b, First[Last[FactorInteger[p]]]], {n, 1, 31}]; b (* Artur Jasinski, Apr 04 2008 *)
lst = {}; Table[First[Last[FactorInteger[FromDigits[Reverse[lst = Join[lst,IntegerDigits[n]]]]]]], {n, 1, 10}] (* Robert Price, Mar 22 2015 *)
  • PARI
    f(n) = my(D = Vec(concat(apply(s->Str(s), [1..n])))); eval(concat(vector(#D, k, D[#D-k+1]))); \\ A138793
a(n) = if(n == 1, 1, vecmax(factor(f(n))[,1])); \\ Daniel Suteu, May 26 2022

Formula

a(n) = A006530(A138793(n)). - Daniel Suteu, May 26 2022

A078998 Choose a(n) so that a(1)+a(2)+...+a(n) = concatenation of n first natural numbers.

Original entry on oeis.org

1, 11, 111, 1111, 11111, 111111, 1111111, 11111111, 111111111, 12222222121, 1222222212101, 122222221210101, 12222222121010101, 1222222212101010101, 122222221210101010101, 12222222121010101010101
Offset: 1

Views

Author

Benoit Cloitre, Jan 12 2003

Keywords

Crossrefs

Cf. A000422, A116504, A007908, A116505, A104759, A138789, A138790, A138793.

Programs

  • Mathematica
    b = {}; a = {}; Do[w = RealDigits[n]; w = First[w]; Do[AppendTo[a, w[[k]]], {k, 1, Length[w]}]; p = FromDigits[a]; AppendTo[b, p], {n, 1, 30}]; c = {}; Do[AppendTo[c, b[[n + 1]] - b[[n]]], {n, 1, Length[b] - 1}]; c (* Artur Jasinski, Mar 30 2008 *)

Formula

a(1)=1; for n>1, a(n) = A007908(n)-A007908(n-1)

A138795 a(n) = (A138793(n+1)-A138793(n))/10^n.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 8, 9, 1, 110, 2100, 31000, 410000, 5100000, 61000000, 710000000, 8100000000, 91000000000, 20000000000, 1200000000000, 22000000000000, 320000000000000, 4200000000000000, 52000000000000000, 620000000000000000
Offset: 1

Views

Author

Artur Jasinski, Mar 30 2008

Keywords

Comments

First differences of A138793 divided by 10^n

Crossrefs

Cf. A000422, A116504, A007908, A116505, A104759, A138789, A138790, A138793, A075019, A075020, A075021, A075022, A138794.

Programs

  • Mathematica
    b = {}; a = {}; Do[w = RealDigits[n]; w = First[w]; Do[AppendTo[a, w[[k]]], {k, 1, Length[w]}]; p = FromDigits[Reverse[a]]; AppendTo[b, p], {n, 1, 61}]; c = {}; Do[AppendTo[c, (b[[n + 1]] - b[[n]])/(10^n)], {n, 1, Length[b] - 1}]; c (*Artur Jasinski*)

Formula

a(n) = A138793(n+1)-A138793(n)
Previous Showing 11-16 of 16 results.

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