A138962 -id:A138962 - cp's OEIS frontend

A075019 a(1) = 1; for n > 1, a(n) = the smallest prime divisor of the number C(n) formed from the concatenation of 1,2,3,... up to n.

1, 2, 3, 2, 3, 2, 127, 2, 3, 2, 3, 2, 113, 2, 3, 2, 3, 2, 13, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 29, 2, 3, 2, 3, 2, 71, 2, 3, 2, 3, 2, 7, 2, 3, 2, 3, 2, 23, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 10386763, 2, 3, 2, 3, 2, 397, 2, 3, 2, 3, 2, 37907, 2, 3, 2, 3, 2, 73, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 37, 2, 3, 2

Offset: 1

Amarnath Murthy, Sep 01 2002

Least prime factor of A007908(n). For 1 < n <= 5000, a(n) < A007908(n), but this should fail infinitely often (assuming standard heuristics). - Charles R Greathouse IV, Apr 10 2014
From Robert Israel, Aug 28 2015: (Start)
a(n) = 2 iff n is even.
a(n) = 3 iff n == 3 or 5 (mod 6).
a(n) = 5 iff n == 25 (mod 30). (End)

			a(5)= 3, 3 is the smallest prime divisor of 12345.

Robert G. Wilson v, Table of n, a(n) for n = 1..1000 (first 120 terms from Robert Israel)

Cf. A000422, A007908, A075020, A104759, A116504, A116505, A138789, A138790, A138960, A138961, A138962.

C:= 1: A[1]:= 1:
for n from 2 to 100 do
C:= C*10^(1+ilog10(n))+n;
F:= map(t -> t[1],ifactors(C,'easy')[2]);
if hastype(F,integer) then A[n]:= min(select(type,F,integer))
else A[n]:= min(numtheory:-factorset(C))
fi
od:
seq(A[n],n=1..100); # Robert Israel, Aug 28 2015

a = {}; b = {}; Do[w = RealDigits[n]; w = First[w]; Do[AppendTo[a, w[[k]]], {k, Length[w]}]; p = FromDigits[a]; AppendTo[b,First[First[FactorInteger[ p]]]], {n, 25}]; b (* Artur Jasinski, Apr 04 2008 *)

lpf(n)=forprime(p=2,1e3,if(n%p==0,return(p))); factor(n)[1,1]
print1(N=1);for(n=2,100,N=N*10^#Str(n)+n; print1(", "lpf(N))) \\ Charles R Greathouse IV, Apr 10 2014

More terms from Sascha Kurz, Jan 03 2003

A075022 a(1) = 1; for n>1, a(n) = the largest prime divisor of the number C(n) formed from the concatenation of 1,2,3,... up to n.

Original entry on oeis.org

1, 3, 41, 617, 823, 643, 9721, 14593, 3803, 1234567891, 630803, 2110805449, 869211457, 205761315168520219, 8230452606740808761, 1231026625769, 584538396786764503, 801309546900123763, 833929457045867563

Offset: 1

Amarnath Murthy, Sep 01 2002

			a(4) = 617 since 1234 = 2*617.

N. J. A. Sloane, Table of n, a(n) for n = 1..56 [First 50 terms from Zak Seidov]

Cf. A075019, A075020, A075021.

Cf. A104759, A000422, A116504, A007908, A116505, A104759, A138789, A138790, A138960, A138961, A138962.

a = {}; b = {}; Do[w = RealDigits[n]; w = First[w]; Do[AppendTo[a, w[[k]]], {k, 1, Length[w]}]; p = FromDigits[a]; AppendTo[b, First[Last[FactorInteger[p]]]], {n, 1, 25}]; b (* Artur Jasinski, Apr 04 2008 *)
Table[FactorInteger[FromDigits[Flatten[IntegerDigits/@Range[n]]]][[-1,1]],{n,20}] (* Harvey P. Dale, Aug 31 2015 *)

More terms from Sascha Kurz, Jan 03 2003

A075020 a(1) = 1; for n>1, a(n) = the smallest prime divisor of the number C(n) formed from the reverse concatenation of 1,2,3,... up to n.

Original entry on oeis.org

1, 3, 3, 29, 3, 3, 19, 3, 3, 7, 3, 3, 17, 3, 3, 23, 3, 3, 17, 3, 3, 13, 3, 3, 11, 3, 3, 23, 3, 3, 7, 3, 3, 89, 3, 3, 29, 3, 3, 11, 3, 3, 52433, 3, 3, 23, 3, 3, 71, 3, 3, 7, 3, 3

Offset: 1

Amarnath Murthy, Sep 01 2002

			a(4)= 29, 29 is the smallest prime divisor of 4321 =29*149

Cf. A075019.

Cf. A104759, A000422, A116504, A007908, A116505, A104759, A138789, A138790, A138960, A138961, A138962.

b = {}; a = {}; Do[w = RealDigits[n]; w = First[w]; Do[AppendTo[a, w[[Length[w] - k + 1]]], {k, 1, Length[w]}]; p = FromDigits[Reverse[a]]; AppendTo[b, First[First[FactorInteger[p]]]], {n, 1, 21}]; b (* Artur Jasinski, Apr 04 2008 *)

More terms from Sascha Kurz, Jan 03 2003

A075021 a(1) = 1; for n>1, a(n) = the largest prime divisor of the number C(n) formed from the concatenation of n, n-1, n-2, n-3, ... down to 1.

Original entry on oeis.org

1, 7, 107, 149, 953, 218107, 402859, 4877, 379721, 54421, 370329218107, 5767189888301, 237927839, 1728836281, 136133374970881, 1190788477118549, 677181889, 399048049, 40617114482123, 629639170774346584751, 2605975408790409767, 65372140114441

Offset: 1

Amarnath Murthy, Sep 01 2002

			a(4)= 149 as 149 is the largest prime divisor of 4321 =29*149

Daniel Suteu, Table of n, a(n) for n = 1..106

Cf. A006530, A000422, A075019, A075020, A075022.

Cf. A104759, A116504, A007908, A116505, A104759, A138789, A138790, A138957, A138960, A138961, A138962.

b = {}; a = {}; Do[w = RealDigits[n]; w = First[w];Do[AppendTo[a, w[[Length[w] - k + 1]]], {k, 1, Length[w]}];p = FromDigits[Reverse[a]];AppendTo[b, First[Last[FactorInteger[p]]]], {n, 1, 21}]; b (* Artur Jasinski, Apr 04 2008 *)
Table[FactorInteger[FromDigits[Flatten[IntegerDigits/@Range[n,1,-1]]]] [[-1,1]],{n,20}] (* Harvey P. Dale, Dec 14 2020 *)

a(n) = if(n==1, 1, vecmax(factor(eval(concat(apply(k->Str(n-k+1), [1..n]))))[, 1])); \\ Daniel Suteu, May 26 2022

a(n) = A006530(A000422(n)). - Daniel Suteu, May 26 2022

More terms from Sascha Kurz, Jan 03 2003

Name edited by Felix Fröhlich, May 26 2022

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

Artur Jasinski, Apr 04 2008

For the smallest prime divisors of A138793 see A138962.

Daniel Suteu and Robert Price, Table of n, a(n) for n = 1..63 (terms a(1)..a(45) from Robert Price)

Cf. A006530, A138793, A138962.

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

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 *)

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

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

cp's OEIS Frontend

A075019 a(1) = 1; for n > 1, a(n) = the smallest prime divisor of the number C(n) formed from the concatenation of 1,2,3,... up to n.

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A075022 a(1) = 1; for n>1, a(n) = the largest prime divisor of the number C(n) formed from the concatenation of 1,2,3,... up to n.

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A075020 a(1) = 1; for n>1, a(n) = the smallest prime divisor of the number C(n) formed from the reverse concatenation of 1,2,3,... up to n.

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A075021 a(1) = 1; for n>1, a(n) = the largest prime divisor of the number C(n) formed from the concatenation of n, n-1, n-2, n-3, ... down to 1.

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

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