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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A205134 s(k)-s(j), where (s(k),s(j)) is the least such pair for which n divides their difference, and s(j)=2*j^2-j, the j-th hexagonal number.

Original entry on oeis.org

5, 14, 9, 44, 5, 30, 14, 152, 9, 30, 22, 60, 13, 14, 30, 560, 17, 90, 38, 60, 21, 22, 46, 216, 25, 78, 27, 140, 29, 30, 62, 2144, 33, 102, 105, 108, 37, 38, 39, 280, 41, 210, 86, 44, 90, 46, 94, 624, 147, 350, 51, 156, 53, 54, 165, 280, 114, 174, 118, 60
Offset: 1

Views

Author

Clark Kimberling, Jan 25 2012

Keywords

Comments

For a guide to related sequences, see A204892.

Crossrefs

Cf. A205130, A204892.

Programs

  • Mathematica
    (See the program at A205130.)

A205142 s(k)-s(j), where (s(k),s(j)) is the least such pair for which n divides their difference, and s(j)=j(3j-1)/2, the j-th pentagonal number.

Original entry on oeis.org

4, 4, 21, 4, 10, 30, 7, 16, 144, 10, 11, 48, 13, 70, 30, 16, 17, 144, 19, 80, 21, 22, 23, 48, 50, 130, 1161, 112, 29, 30, 31, 64, 66, 34, 35, 144, 37, 190, 39, 80, 41, 84, 43, 308, 225, 46, 47, 48, 196, 50, 102, 260, 53, 1242, 110, 112, 57, 58, 59, 120
Offset: 1

Views

Author

Clark Kimberling, Jan 25 2012

Keywords

Comments

For a guide to related sequences, see A204892.

Crossrefs

Cf. A205138, A204892.

Programs

  • Mathematica
    (See the program at A205138.)

A205143 (1/n)*A205142(n).

Original entry on oeis.org

4, 2, 7, 1, 2, 5, 1, 2, 16, 1, 1, 4, 1, 5, 2, 1, 1, 8, 1, 4, 1, 1, 1, 2, 2, 5, 43, 4, 1, 1, 1, 2, 2, 1, 1, 4, 1, 5, 1, 2, 1, 2, 1, 7, 5, 1, 1, 1, 4, 1, 2, 5, 1, 23, 2, 2, 1, 1, 1, 2, 1, 5, 4, 1, 1, 1, 1, 7, 1, 1, 1, 2, 1, 5, 1, 5, 2, 5, 1, 1
Offset: 1

Views

Author

Clark Kimberling, Jan 25 2012

Keywords

Comments

For a guide to related sequences, see A204892.

Crossrefs

Cf. A205138, A204892.

Programs

  • Mathematica
    (See the program at A205138.)

A205151 a(n) = A205150(n)/n.

Original entry on oeis.org

9, 10, 3, 5, 4, 7, 6, 16, 1, 2, 6, 9, 6, 3, 12, 8, 6, 6, 6, 1, 2, 3, 10, 6, 34, 3, 4, 11, 1, 6, 2, 4, 2, 3, 71, 3, 10, 3, 2, 9, 6, 1, 5, 7, 4, 5, 19, 3, 6, 17, 2, 17, 12, 2, 36, 11, 2, 4, 10, 3, 50, 1, 12, 2, 31, 1, 6, 13, 74, 23, 1, 2, 50, 5, 24, 23, 4, 1, 8
Offset: 1

Views

Author

Clark Kimberling, Jan 25 2012

Keywords

Comments

For a guide to related sequences, see A204892.

Links

Crossrefs

Cf. A205146, A204892.

Programs

  • Mathematica
    (See the program at A205146.)
  • PARI
    s(m) = prime(m)*prime(m+1);
isok(k, n) = my(sk=s(k)); for (j=1, k-1, if (!Mod(sk-s(j), n), return (j)));
a(n) = my(k=1, x); while (!(j=isok(k, n)), k++); (s(k) - s(j))/n; \\ Michel Marcus, Jul 23 2021

Extensions

More terms from Michel Marcus, Jul 23 2021

A205372 Least s(k) such that n divides s(k)-s(j) for some jA024675.

Original entry on oeis.org

6, 6, 9, 12, 9, 12, 18, 12, 15, 26, 15, 18, 30, 18, 21, 34, 21, 30, 34, 26, 30, 26, 50, 30, 34, 30, 39, 34, 50, 34, 76, 50, 39, 60, 39, 42, 76, 42, 45, 86, 45, 60, 64, 50, 60, 50, 56, 60, 64, 56, 60, 56, 129, 60, 64, 60, 69, 64, 93, 64, 76, 134, 69, 76, 69, 72, 76
Offset: 1

Views

Author

Clark Kimberling, Jan 26 2012

Keywords

Comments

For a guide to related sequences, see A204892.
a(n) >= n+4, with equality if and only if n+4 is in A024675.

Links

Crossrefs

Cf. A024675, A205153, A204892.

Programs

  • Maple
    N:= 200: # for terms before the first > the greatest prime <= N
P:= select(isprime, [seq(i,i=3..N,2)]):
S:= (P[1..-2]+P[2..-1])/2:
f:= proc(n) local T,R,i;
   T:= S mod n;
   R:= {}:
   for i from 1 to nops(T)-1 do
     R:= R union {T[i]};
     if member(T[i+1],R) then return S[i+1] fi;
   od;
   FAIL
end proc:
Res:= NULL:
for n from 1 do
  v:= f(n);
  if v = FAIL then break fi;
  Res:= Res, v
od:
Res; # Robert Israel, Sep 09 2020
  • Mathematica
    (See the program at A205153.)

A205374 s(k)-s(j), where (s(k),s(j)) is the least such pair for which n divides their difference, and s(j)=(prime(j+1) + prime(j+2))/2.

Original entry on oeis.org

2, 2, 3, 8, 5, 6, 14, 8, 9, 20, 11, 12, 26, 14, 15, 16, 17, 18, 19, 20, 21, 22, 46, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 80, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69
Offset: 1

Views

Author

Clark Kimberling, Jan 26 2012

Keywords

Comments

For a guide to related sequences, see A204892.

Crossrefs

Cf. A205153, A204892.

Programs

  • Mathematica
    (See the program at A205153.)

A205379 The index j

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 3, 1, 2, 2, 5, 1, 6, 3, 1, 2, 8, 2, 9, 2, 1, 5, 11, 1, 3, 6, 2, 3, 14, 1, 15, 4, 3, 8, 2, 2, 18, 9, 4, 2, 20, 1, 21, 5, 1, 11, 23, 1, 4, 3, 6, 6, 26, 2, 1, 3, 7, 14, 29, 1
Offset: 1

Views

Author

Clark Kimberling, Jan 26 2012

Keywords

Comments

For a guide to related sequences, see A204892.

Crossrefs

Cf. A205378, A204892.

Programs

  • Mathematica
    (See the program at A205378.)

A205382 s(k)-s(j), where (s(k),s(j)) is the least such pair for which n divides their difference, and s(j)=(2j-1)^2.

Original entry on oeis.org

8, 8, 24, 8, 40, 24, 56, 8, 72, 40, 88, 24, 104, 56, 120, 16, 136, 72, 152, 40, 168, 88, 184, 24, 200, 104, 216, 56, 232, 120, 248, 32, 264, 136, 280, 72, 296, 152, 312, 40, 328, 168, 344, 88, 360, 184, 376, 48, 392, 200, 408, 104, 424, 216, 440, 56, 456
Offset: 1

Views

Author

Clark Kimberling, Jan 26 2012

Keywords

Comments

Duplicate of A109049? For a guide to related sequences, see A204892.

Crossrefs

Cf. A205383, A205378, A204892, A109049.

Programs

  • Mathematica
    (See the program at A205378.)

Formula

a(n) = n*A205383(n). - Luce ETIENNE, Feb 19 2020

A205387 The index j

Original entry on oeis.org

1, 1, 1, 2, 3, 5, 2, 2, 1, 5, 6, 5, 4, 5, 5, 2, 1, 3, 6, 4, 5, 6, 3, 5, 3, 7, 2, 5, 3, 5, 10, 2, 6, 1, 1, 3, 1, 6, 7, 4, 2, 5, 14, 6, 3, 3, 5, 5, 1, 4
Offset: 1

Views

Author

Clark Kimberling, Jan 27 2012

Keywords

Comments

For a guide to related sequences, see A204892.

Crossrefs

Cf. A205386, A204892.

Programs

  • Mathematica
    (See the program at A205386.)

A205388 Least s(k) such that n divides s(k)-s(j) for some j

Original entry on oeis.org

3, 3, 10, 35, 35, 462, 10, 35, 10, 1716, 1716, 462, 126, 462, 1716, 35, 35, 24310, 1716, 6435, 462, 1716, 92378, 462, 35, 24310, 462, 462, 126, 1716, 352716, 35, 1716, 35, 1716, 24310, 24310, 1716, 6435, 6435, 126, 462, 77558760, 24310, 24310
Offset: 1

Views

Author

Clark Kimberling, Jan 27 2012

Keywords

Comments

For a guide to related sequences, see A204892.

Links

Crossrefs

Cf. A205386, A204892.

Programs

  • Maple
    N:= 100: # for a(1)..a(N)
S:=proc(j) option remember; binomial(2*j,j)/2 end proc:
A:= Vector(N): T:= {$1..N}:
for k from 2 while T <> {} do
  for j from 1 to k-1 while T <>{} do
    w:= S(k)-S(j);
    d:= select(t -> w mod t = 0, T);
    A[convert(d,list)]:= S(k);
    T:= T minus d;
  od;
od;
convert(A,list); # Robert Israel, Aug 28 2019
  • Mathematica
    (See the program at A205386.)
Previous Showing 91-100 of 248 results. Next

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