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.

A104534 Indices of prime tetranacci numbers.

Original entry on oeis.org

3, 7, 11, 12, 36, 56, 401, 2707, 8417, 14096, 31561, 50696, 53192, 155182
Offset: 1

Views

Author

Eric W. Weisstein, Mar 13 2005

Keywords

Links

Crossrefs

Cf. A000078, A104535.

Formula

A000078(a(n) + 2) = A104535(n). - Andrew Howroyd, Oct 08 2024

Extensions

a(14)=155182 found by Eric W. Weisstein, Oct 28 2005

A113244 Prime differences of tetranacci numbers.

Original entry on oeis.org

2, 3, 7, 11, 13, 41, 79, 107, 179, 193, 293, 397, 769, 1489, 2099, 2843, 2857, 5507, 5521, 9181, 10463, 10663, 10667, 19079, 39619, 76423, 126743, 146539, 147283, 147311, 281081, 283949, 547229, 771073, 3919171, 3919543, 3919943, 7555879, 7555927, 10644589, 14564477
Offset: 1

Views

Author

Jonathan Vos Post, Oct 19 2005; corrected Oct 20 2005

Keywords

Comments

A113188-A113194 deal with difference sets of Fibonacci numbers and Lucas numbers and primes in those difference sets. A113238-A113239 deal with the difference set of tribonacci numbers and primes in that difference set.

Examples

			a(1) = 2 because 4 - 2 = 2 where 4 and 2 are tetranacci numbers.
a(2) = 3 because 4 - 1 = 3 where 4 and 1 are tetranacci numbers.
a(3) = 7 because 8 - 1 = 7 where 8 and 1 are tetranacci numbers.
a(4) = 11 because 15 - 4 = 11 where 15 and 4 are tetranacci numbers.
a(5) = 13 because 15 - 2 = 13 where 15 and 2 are tetranacci numbers.

Crossrefs

Cf. A000040, A000078, A113188-A113194, A113238, A113239, A113243.

Programs

  • Maple
    isA113244 := proc(n)
    isprime(n) and isA113243(n) ;
end proc:
for n from 1 do
    p := ithprime(n) ;
    if isA113244(p) then
        printf("%d\n",p) ;
    end if;
end do: # R. J. Mathar, Oct 04 2014

Formula

{a(n)} = intersection of A000040 and A113243. {a(n)} = primes in the difference set of tetranacci sequence A000078, excluding prime tetranacci numbers A104535.

Extensions

281081 inserted by R. J. Mathar, Oct 04 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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