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.

A282769 n/7 analog of Keith numbers.

Original entry on oeis.org

301, 602, 1113, 4942, 478205, 23942940, 47885880, 178114489749
Offset: 1

Views

Author

Paolo P. Lava, Feb 27 2017

Keywords

Comments

Like Keith numbers but starting from n/7 digits to reach n.
Consider the digits of n/7. Take their sum and repeat the process deleting the first addend and adding the previous sum. The sequence lists the numbers that after some iterations reach a sum equal to themselves.
If it exists, a(9) > 10^12. - Lars Blomberg Mar 07 2017

Examples

			1113/7 = 159:
    1 +   5 +   9 =   15;
    5 +   9 +  15 =   29;
    9 +  15 +  29 =   53;
   15 +  29 +  53 =   97;
   29 +  53 +  97 =  179;
   53 +  97 + 179 =  329;
   97 + 179 + 329 =  605;
  179 + 329 + 605 = 1113.

Crossrefs

Cf. A282757 - A282765, A282766 - A282768.

Programs

  • Maple
    with(numtheory): P:=proc(q,h,w) local a, b, k, n, t, v; v:=array(1..h);
for n from 1/w by 1/w to q do a:=w*n; b:=ilog10(a)+1; if b>1 then
for k from 1 to b do v[b-k+1]:=(a mod 10); a:=trunc(a/10); od; t:=b+1; v[t]:=add(v[k], k=1..b);
while v[t]
  • Mathematica
    With[{n = 7}, Select[Range[10 n, 10^6, n], Function[k, Last@ NestWhile[Append[Rest@ #, Total@ #] &, IntegerDigits[k/n], Total@ # <= k &] == k]]] (* Michael De Vlieger, Feb 27 2017 *)

Extensions

a(8) from Lars Blomberg, Mar 07 2017

A282768 n/5 analog of Keith numbers.

Original entry on oeis.org

55, 110, 165, 220, 275, 330, 385, 440, 495, 530, 47270, 119710, 685385, 21526000, 6055017240
Offset: 1

Views

Author

Paolo P. Lava, Feb 27 2017

Keywords

Comments

Like Keith numbers but starting from n/5 digits to reach n.
Consider the digits of n/5. Take their sum and repeat the process deleting the first addend and adding the previous sum. The sequence lists the numbers that after some iterations reach a sum equal to themselves.
If it exists, a(16) > 10^12. - Lars Blomberg Mar 07 2017

Examples

			530/5 = 106:
   1 +   0 +   6 =   7;
   0 +   6 +   7 =  13;
   6 +   7 +  13 =  26;
   7 +  13 +  26 =  46;
  13 +  26 +  46 =  85;
  26 +  46 +  85 = 157;
  46 +  85 + 157 = 288;
  85 + 157 + 288 = 530.

Crossrefs

Cf. A282757 - A282765, A282766, A282767, A282769.

Programs

  • Maple
    with(numtheory): P:=proc(q,h,w) local a, b, k, n, t, v; v:=array(1..h);
for n from 1/w by 1/w to q do a:=w*n; b:=ilog10(a)+1; if b>1 then
for k from 1 to b do v[b-k+1]:=(a mod 10); a:=trunc(a/10); od; t:=b+1; v[t]:=add(v[k], k=1..b);
while v[t]
  • Mathematica
    With[{n = 5}, Select[Range[10 n, 10^6, n], Function[k, Last@ NestWhile[Append[Rest@ #, Total@ #] &, IntegerDigits[k/n], Total@ # <= k &] == k]]] (* Michael De Vlieger, Feb 27 2017 *)

Extensions

a(15) from Lars Blomberg, Mar 07 2017

A282767 n/3 analog of Keith numbers.

Original entry on oeis.org

45, 609, 1218, 1827, 3213, 21309, 28206, 29319, 31917, 39333, 47337, 78666, 102090, 117999, 204180, 406437, 302867592, 4507146801, 5440407522
Offset: 1

Views

Author

Paolo P. Lava, Feb 27 2017

Keywords

Comments

Like Keith numbers but starting from n/3 digits to reach n.
Consider the digits of n/3. Take their sum and repeat the process deleting the first addend and adding the previous sum. The sequence lists the numbers that after some iterations reach a sum equal to themselves.
If it exists, a(20) > 10^12. - Lars Blomberg Mar 13 2017

Examples

			609/3 = 203:
2 + 0 + 3 = 5;
0 + 3 + 5 = 8;
3 + 5 + 8 = 16;
5 + 8 + 16 = 29;
8 + 16 + 29 = 53;
16 + 29 + 53 = 98;
29 + 53 + 98 = 180;
53 + 98 + 180 = 331;
98 + 180 + 331 = 609.

Crossrefs

Cf. A282757 - A282765, A282766, A282768, A282769.

Programs

  • Maple
    with(numtheory): P:=proc(q,h,w) local a, b, k, n, t, v; v:=array(1..h);
for n from 1/w by 1/w to q do a:=w*n; b:=ilog10(a)+1; if b>1 then
for k from 1 to b do v[b-k+1]:=(a mod 10); a:=trunc(a/10); od; t:=b+1; v[t]:=add(v[k], k=1..b);
while v[t]
  • Mathematica
    With[{n = 3}, Select[Range[10 n, 10^6, n], Function[k, Last@ NestWhile[Append[Rest@ #, Total@ #] &, IntegerDigits[k/n], Total@ # <= k &] == k]]] (* Michael De Vlieger, Feb 27 2017 *)

Extensions

a(17)-a(19) from Lars Blomberg, Mar 13 2017

A284493 Analog of Keith numbers based on digits of sum of anti-divisors.

Original entry on oeis.org

18, 26, 40, 93, 95, 122, 227, 5640, 8910, 15481, 56028, 117056, 282103, 394608, 2059983, 3775282, 3804607, 5005918, 10390740, 31753906, 42117745, 67170923, 98908536, 176337241
Offset: 1

Views

Author

Paolo P. Lava, Mar 28 2017

Keywords

Comments

Consider the digits of the sum of anti-divisors of n. Take their sum and repeat the process deleting the first addend and adding the previous sum. The sequence lists the numbers that after some iterations reach a sum equal to themselves.

Examples

			Sum of the anti-divisors of 18 is 28: 2 + 8 = 10, 8 + 10 = 18.
Sum of the anti-divisors of 93 is 140: 1 + 4 + 0 = 5, 4 + 0 + 5 = 9, 0 + 5 + 9 = 14, 5 + 9 + 14 = 28, 9 + 14 + 28 = 51, 14 + 28 + 51 = 93.

Crossrefs

Cf. A066272, A282757 - A282765, A282766 - A282769.

Programs

  • Maple
    with(numtheory): P:=proc(q,h) local a,b,j,k,n,t,v; v:=array(1..h);
for n from 10^6 to q do k:=0; j:=n; while j mod 2 <> 1 do
k:=k+1; j:=j/2; od; a:=sigma(2*n+1)+sigma(2*n-1)+sigma(n/2^k)*2^(k+1)-6*n-2;
b:=ilog10(a)+1; if b>1 then for k from 1 to b do
v[b-k+1]:=(a mod 10); a:=trunc(a/10); od; t:=b+1;
v[t]:=add(v[k], k=1..b); while v[t]

Extensions

a(18)-a(24) from Georg Fischer, Oct 26 2019
Showing 1-4 of 4 results.

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