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.

A251551 a(n) = A251546(n) - A251549(n).

Original entry on oeis.org

-1, 1, -1, 1, 1, 1, 1, 1, -1, 3, 3, 3, 3, 3, -1, 7, 7, 7, 7, 7, 7, 5, 1, 1, 1, 1, 1, 1, 1, -1, 5, 5, 11, 11, 11, 11, 11, 11, 19, 19, 21, 21, 17, 17, 17, 17, 17, 23, 23, 23, 17, 17, 17, 17, 17, 25, 25, 25, 25, 25, 23, 17
Offset: 1

Views

Author

N. J. A. Sloane, Dec 18 2014

Keywords

Links

Crossrefs

Cf. A098550, A247253, A251416, A251417, A251546-A251552.

Programs

A251550 a(n) = (A251549(n)-1)/2.

Original entry on oeis.org

1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 6, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 11, 11, 11, 11, 11, 11, 11, 11, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 18, 18, 18, 18, 18
Offset: 1

Views

Author

N. J. A. Sloane, Dec 18 2014

Keywords

Links

Crossrefs

Cf. A098550, A247253, A251416, A251417, A251546-A251552.

Programs

A251416 a(n) = smallest number not in {A098550(1), A098550(2), ..., A098550(n)}.

Original entry on oeis.org

2, 3, 4, 5, 5, 5, 5, 5, 6, 7, 7, 7, 7, 7, 10, 11, 11, 11, 11, 11, 11, 13, 17, 17, 17, 17, 17, 17, 17, 18, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 23, 23, 23, 23, 23, 23, 23, 23, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 31
Offset: 1

Views

Author

N. J. A. Sloane, Dec 03 2014

Keywords

Comments

a(n) = smallest missing number in A098550 once we have found A098550(n).
Bradley Klee conjectures that after a(30)=18, all further terms are primes, that every prime appears, and the primes appear in increasing order.

References

  • Bradley Klee, Posting to Sequence Fans Mailing List, Dec 03 2014

Links

Crossrefs

Cf. A098550, A251415. See A251417 for lengths of runs.
Cf. A251595 (distinct terms).
Cf. A251546, A251549.

Programs

  • Haskell
    import Data.List (delete)
a251416 n = a251416_list !! (n-1)
a251416_list = 2 : 3 : f 2 3 [4..] where
   f u v ws = h ws where
     h (x:xs) = if gcd x u > 1 && gcd x v == 1
                   then (head ws) : f v x (delete x ws) else h xs
-- Reinhard Zumkeller, Dec 05 2014
  • Maple
    # This produces the first 100 terms. Uses b1 = list of terms in A098550, from b-file
b2:={$3..5000}:
b3:=[2]:
for i from 2 to 100 do
b2:=remove('x->x=b1[i]',b2):
b3:=[op(b3),b2[1]];
od:
b3;
  • Mathematica
    terms = 100;
f[lst_List] := Block[{k = 4}, While[GCD[lst[[-2]], k] == 1 || GCD[lst[[-1]], k] > 1 || MemberQ[lst, k], k++]; Append[lst, k]];
A098550 = Nest[f, {1, 2, 3}, terms-3];
a[1] = 2;
a[n_] := a[n] = For[k = a[n - 1], True, k++, If[FreeQ[A098550[[1 ;; n]], k], Return[k]]];
Array[a, terms] (* Jean-François Alcover, Aug 01 2018, after Robert G. Wilson v *)

Formula

a(n) = Min{A251546(n), A251549(n)}. - Reinhard Zumkeller, Dec 19 2014

A251546 a(n) = smallest even number not in {A098550(1), A098550(2), ..., A098550(n)}.

Original entry on oeis.org

2, 4, 4, 6, 6, 6, 6, 6, 6, 10, 10, 10, 10, 10, 10, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 24, 24, 30, 30, 30, 30, 30, 30, 38, 38, 40, 40, 40, 40, 40, 40, 40, 46, 46, 46, 46, 46, 46, 46, 46, 54, 54, 54
Offset: 1

Views

Author

N. J. A. Sloane, Dec 18 2014

Keywords

Comments

A251416(n) = Min{a(n), A251549(n)}. - Reinhard Zumkeller, Dec 19 2014

Links

Crossrefs

Cf. A098550, A247253, A251416, A251417, A251547, A251548, A251549, A251550, A251551, A251552.
See also A251557, A251558, A251559.

Programs

  • Haskell
    import Data.List ((\\))
a251546 n = head $ [2, 4 ..] \\ filter even (take n a098550_list)
-- Reinhard Zumkeller, Dec 19 2014
  • Mathematica
    terms = 100;
f[lst_List] := Block[{k = 4}, While[GCD[lst[[-2]], k] == 1 || GCD[lst[[-1]], k] > 1 || MemberQ[lst, k], k++]; Append[lst, k]];
A098550 = Nest[f, {1, 2, 3}, terms - 3];
a[1] = 2;
a[n_] := a[n] = For[k = a[n-1], True, k += 2, If[FreeQ[A098550[[1;;n]], k], Return[k]]];
Array[a, terms] (* Jean-François Alcover, Aug 01 2018, after Robert G. Wilson v *)

A247253 First differences of A251239.

Original entry on oeis.org

1, 6, 6, 7, 1, 7, 13, 8, 10, 1, 17, 8, 1, 13, 13, 13, 5, 10, 11, 5, 9, 8, 19, 10, 11, 7, 11, 5, 9, 27, 9, 13, 5, 23, 5, 9, 17, 9, 11, 11, 7, 21, 9, 7, 5, 17, 27, 11, 7, 9, 17, 5, 13, 9, 21, 11, 7, 13, 9, 9, 17, 31, 7, 7, 9, 29, 9, 25, 5, 7, 13, 15, 15, 11
Offset: 1

Views

Author

Reinhard Zumkeller, Dec 02 2014

Keywords

Comments

a(n) = A251239(n+1) - A251239(n);
Conjecture 1: a(n) > 0, since presumably primes occur in A098550 in natural order;
Conjecture 2: it seems that a(n) = 1 only for n = 1, 5, 10 and 13;
Conjecture 3: a(n) - 1 = number of composite terms between prime(n) and prime(n+1) in A098550;
Conjecture 4: a(n) = A251417(n+5) for n>7. (The first four conjectures are due to Reinhard Zumkeller.)
Conjecture 5: Apart from first term, this is equal to the sequence of run lengths in A251549. These run lengths begin 2, 6, 6, 7, 1, 7, 13, 8, 10, 1, 17, 8, 1, 13, 13, 13, 5, 10, 11, 5, 9, ... . - N. J. A. Sloane, Dec 18 2014

Links

Crossrefs

Cf. A251239, A098550, A002808, A251417, A251549.

Programs

  • Haskell
    a247253 n = a247253_list !! (n-1)
a247253_list = zipWith (-) (tail a251239_list) a251239_list
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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