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.

A104412 Number of prime factors, with multiplicity, of the pentanacci numbers A001591.

Original entry on oeis.org

0, 0, 1, 2, 3, 4, 1, 1, 5, 3, 5, 6, 2, 4, 6, 5, 9, 6, 2, 2, 6, 4, 6, 7, 1, 3, 3, 6, 4, 7, 4, 2, 7, 3, 9, 7, 3, 2, 2, 8, 9, 8, 2, 4, 11, 7, 9, 7, 7, 2, 4, 5, 6, 7, 3, 2, 7, 7, 13, 8, 4, 5, 5, 6, 10, 5, 4, 7, 11, 7, 8, 9, 4, 5, 4, 8, 7, 8, 4, 5, 6, 5, 10, 12, 2, 4, 5, 9, 12, 11, 7, 4, 13
Offset: 4

Views

Author

Jonathan Vos Post, Mar 05 2005

Keywords

Comments

Prime pentanacci numbers (A105757) correspond to 1s in the sequence, semiprimes to 2, and so forth.

Links

Crossrefs

Cf. A001591, A001222, A104411.

Programs

  • Mathematica
    PrimeOmega/@Drop[LinearRecurrence[{1,1,1,1,1},{0,0,0,0,1},100],4] (* Harvey P. Dale, Mar 30 2019 *)

Formula

a(n) = A001222(A001591(n)). a(n) = bigomega(A001591(n)).

Extensions

Offset corrected by Joerg Arndt, Dec 19 2020

A105756 Indices of prime Fibonacci 5-step numbers, A001591.

Original entry on oeis.org

3, 7, 8, 25, 146, 169, 182, 751, 812, 1507, 1591, 3157, 3752, 10651, 12740, 71804, 155953
Offset: 1

Views

Author

T. D. Noe, Apr 22 2005

Keywords

Comments

No other n < 44000.
The Noe and Post reference below utilizes a scheme for its indices which differs by 3 from the indices in A001591. - Robert Price, Oct 13 2014
The sequence is similar to A248757 which uses the indexing scheme starting at 0 as defined by A001591. - Robert Price, Oct 13 2014
a(18) > 2*10^5. - Robert Price, Oct 13 2014

Links

Crossrefs

Cf. A105757 (prime Fibonacci 5-step numbers).

Programs

  • Mathematica
    a = {1, 0, 0, 0, 0}; lst = {}; Do[s = Plus @@ a; a = RotateLeft[a];
  a[[-1]] = s; If[PrimeQ[s], AppendTo[lst, n]], {n, 44000}]; lst
Flatten[Position[LinearRecurrence[{1,1,1,1,1},{0,0,0,0,1},13000],?PrimeQ]]-4 (* _Harvey P. Dale, Mar 06 2023 *)

Extensions

Restored original sequence after reconsideration and added a(16)-a(17) by Robert Price, Oct 13 2014

A105758 Indices of prime hexanacci (or Fibonacci 6-step) numbers A001592 (using offset -4).

Original entry on oeis.org

3, 36, 37, 92, 660, 6091, 8415, 11467, 13686, 38831, 49828, 97148
Offset: 1

Views

Author

T. D. Noe, Apr 22 2005

Keywords

Comments

No other n < 30000.
This sequence uses the convention of the Noe and Post reference. Their indexing scheme differs by 4 from the indices in A001592. Sequence A249635 lists the indices of the same primes (A105759) using the indexing scheme as defined in A001592. - Robert Price, Nov 02 2014 [Edited by M. F. Hasler, Apr 22 2018]
a(13) > 3*10^5. - Robert Price, Nov 02 2014

Links

Crossrefs

Cf. A105759 (prime Fibonacci 6-step numbers), A249635 (= a(n) + 4), A001592.
Cf. A000045, A000073, A000078 (and A001631), A001591, A122189 (or A066178), A079262, A104144, A122265, A168082, A168083 (Fibonacci, tribonacci, tetranacci numbers and other generalizations).
Cf. A005478, A092836, A104535, A105757, A105761, ... (primes in these sequence).
Cf. A001605, A303263, A303264 (and A104534 and A247027), A248757 (and A105756), ... (indices of primes in A000045, A000073, A000078, ...).

Programs

  • Mathematica
    a={1, 0, 0, 0, 0, 0}; lst={}; Do[s=Plus@@a; a=RotateLeft[a]; a[[ -1]]=s; If[PrimeQ[s], AppendTo[lst, n]], {n, 30000}]; lst

Formula

a(n) = A249635(n) - 4. A105759(n) = A001592(A249635(n)) = A001592(a(n) + 4). - M. F. Hasler, Apr 22 2018

Extensions

a(10)-a(12) from Robert Price, Nov 02 2014
Edited by M. F. Hasler, Apr 22 2018

A303264 Indices of primes in tetranacci sequence A000078.

Original entry on oeis.org

5, 9, 13, 14, 38, 58, 403, 2709, 8419, 14098, 31563, 50698, 53194, 155184
Offset: 1

Views

Author

M. F. Hasler, Apr 18 2018

Keywords

Comments

T = A000078 is defined by T(n) = Sum_{k=1..4} T(n-k), T(3) = 1, T(n) = 0 for n < 3.
The largest terms correspond to unproven probable primes T(a(n)).

Crossrefs

Cf. A000045, A000073, A000078, A001591, A001592, A122189 (or A066178), ... (Fibonacci, tribonacci, tetranacci numbers).
Cf. A005478, A092836, A104535, A105757, A105759, A105761, ... (primes in Fibonacci numbers and above generalizations).
Cf. A001605, A303263, A303264, A248757, A249635, ... (indices of primes in A000045, A000073, A000078, ...).
Cf. A247027: Indices of primes in the tetranacci sequence A001631 (starting 0, 0, 1, 0...), A104534 (a variant: a(n) - 2), A105756 (= A248757 - 3), A105758 (= A249635 - 4).

Programs

  • PARI
    a(n,N=5,S=vector(N,i,i>N-2))={for(i=N,oo,ispseudoprime(S[i%N+1]=2*S[(i-1)%N+1]-S[i%N+1])&&!n--&&return(i))}

Formula

a(n) = A104534(n) + 2.
Showing 1-4 of 4 results.

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