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.

A078284 a(n) = A078283(n)/n.

Original entry on oeis.org

1, 5, 34, 253, 2024, 16867, 144575, 1265032, 11235584, 101120256, 919272960, 8342666880, 77009232720, 715008573240, 6667341335024, 62500632501585, 588241236472080, 5555611677791867, 52632110631712424, 500005051001268028
Offset: 1

Views

Author

Amarnath Murthy, Nov 25 2002

Keywords

Crossrefs

Extensions

More terms from Sascha Kurz, Jan 04 2003

A078282 a(1) = 1, a(n) is the smallest multiple of n which begins with a(n-1) and is greater than a(n-1).

Original entry on oeis.org

1, 10, 102, 1020, 10200, 102000, 1020005, 10200056, 102000564, 1020005640, 10200056405, 1020005640504, 10200056405045, 1020005640504508, 10200056405045085, 1020005640504508512, 10200056405045085129
Offset: 1

Views

Author

Amarnath Murthy, Nov 25 2002

Keywords

Comments

By continuing to delete suitable digits starting from LSD leaves a multiple of n-1, n-2,...up to 1.

Crossrefs

Cf. A078283.

Extensions

More terms from Sascha Kurz, Jan 04 2003

A336399 a(1) = 1, a(n) is the smallest number such that the concatenation a(1)a(2)...a(n) is divisible by lcm(1..n).

Original entry on oeis.org

1, 0, 2, 0, 0, 0, 360, 0, 1680, 0, 35280, 0, 332640, 0, 0, 0, 8648640, 0, 306306000, 0, 0, 0, 232792560, 0, 0, 0, 26771144400, 0, 481880599200, 0, 41923612130400, 0, 0, 0, 0, 0, 5487335009956800, 0, 0, 0, 245774847024907200, 0, 8105227020364874400, 0, 0, 0, 452140231622516236800, 0, 3984485791173424336800, 0
Offset: 1

Views

Author

Eder Vanzei, Jul 20 2020

Keywords

Examples

			a(7) = 360 as the smallest positive integer k such that the concatenation a(1)a(2)..a(6)k is divisible by lcm(1..7) = 420. - _David A. Corneth_, Jul 21 2020
		

Crossrefs

Cf. A336401 (corresponding numbers), A003418 (LCM's).

Programs

  • Maple
    N:= 1: R:= 1: C:= 1:
    for n from 2 to 60 do
      N:= ilcm(N,n);
      for d from 1 do
        x:= -C*10^d mod N;
        if x = 0 then lx:= 1 else lx:= 1+ilog10(x) fi;
        if lx = d then
           R:= R,x;
           C:= C*10^d+x;
           break
        elif lx < d then
           k:= ceil((10^(d-1)-x)/N);
           x:= x + k*N;
           if x < 10^d then
             R:= R,x;
             C:= C*10^d+x;
             break
        fi fi
    od; od:
    R; # Robert Israel, Sep 16 2020
  • PARI
    a(n) = {if(n==1,return(1));for(n1 = 0, oo, ; k[n]=eval(concat(Str(k[n-1]), n1)); n2=0; for(n3 = 1, n, if(k[n] % n3 == 0, n2+=1; if(n2==n, return(k[n])))))};
    k = vector(10000);print1(k[1]=1,", ");for(j=1, 20, print1(a(j+1) - a(j)*10^(length(Str(a(j+1))) - length(Str(a(j)))), ", "))
    
  • PARI
    \\ See Corneth link. David A. Corneth, Jul 21 2020

Extensions

a(27)-a(50) from David A. Corneth, Jul 20 2020

A080502 a(1) = 1, a(n) = smallest multiple of n that can be obtained by inserting digits anywhere in a(n-1) if necessary.

Original entry on oeis.org

1, 10, 102, 1012, 10120, 101202, 1012025
Offset: 1

Views

Author

Amarnath Murthy, Mar 19 2003

Keywords

Examples

			a(4) = 1012 hence a(5)=10120 and a(6) = 101202.
		

Crossrefs

Variant of A078283. [From R. J. Mathar, Sep 19 2008]

A336401 a(n) = a(n-1) concatenated with the smallest number k, such that a(n) is divisible by lcm(1..n).

Original entry on oeis.org

1, 10, 102, 1020, 10200, 102000, 102000360, 1020003600, 10200036001680, 102000360016800, 10200036001680035280, 102000360016800352800, 102000360016800352800332640, 1020003600168003528003326400
Offset: 1

Views

Author

Eder Vanzei, Jul 20 2020

Keywords

Crossrefs

Programs

  • PARI
    a(n)={if(n==1,return(1));for(n1=0,oo,k=eval(concat(Str(a(n-1)),n1));n2=0;for(n3=1,n,if(k%n3==0,n2+=1;if(n2==n,return(k)))))};
Showing 1-5 of 5 results.