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.

A101757 Indices of semiprimes in A000073.

Original entry on oeis.org

5, 12, 18, 42, 44, 50, 58, 67, 74, 83, 90, 95, 126, 142, 194, 210, 211, 275, 367, 382, 479, 655, 734, 818, 839, 926, 939, 1047
Offset: 1

Views

Author

Jonathan Vos Post and Ray Chandler, Dec 26 2004

Keywords

Comments

a(29) >= 1091. A000073(1091) is a 288-digit composite number with unknown factorization. Other possible terms are 1390, 1630, 2034, 2131, 2339, ... - Tyler Busby, Feb 09 2023

Links

  • Eric Weisstein's World of Mathematics, Semiprime

Crossrefs

Cf. A000073, A001358, A101758.
Equivalent sequence for primes: A303263.

Programs

Formula

A000073(a(n)) = A101758(n).

Extensions

More terms from David Wasserman, Apr 03 2008

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.

A122991 Indices of primes in tribonacci sequence A000073, minus 2.

Original entry on oeis.org

2, 4, 5, 9, 85, 96, 213, 800, 4200, 18697, 96877
Offset: 1

Views

Author

Artur Jasinski, Oct 28 2006

Keywords

Comments

Also, indices of primes in A282718.

Crossrefs

Cf. A000073, A092835, A092836, A282718, A303263.

Formula

A000073(a(n) + 2) = A092836(n).
a(n) = A303263(n) - 2 = A092835(n) - 1.

Extensions

Name corrected and a(10)-a(11) added by Andrew Howroyd, Oct 10 2024
Showing 1-4 of 4 results.

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