A105762 -id:A105762 - cp's OEIS frontend

A104576 Indices of primes in A001644 (the Lucas 3-step numbers).

2, 3, 4, 7, 8, 9, 10, 12, 20, 30, 33, 66, 76, 77, 82, 87, 98, 180, 205, 360, 553, 719, 766, 1390, 1879, 1999, 4033, 5620, 16506, 17436, 23676, 24428, 27758, 31932, 58199, 67661, 85040, 102023, 185595

Offset: 1

T. D. Noe, Mar 16 2005

The sequence of generalized tribonacci numbers is defined as beginning with 1, 3, 7. Subsequent terms are the sum of the previous three terms. Note that the sequence of these generalized tribonacci numbers has many more primes than the tribonacci sequence A000073 (whose prime indices are in A092835).

a(40) > 2*10^5. - Robert Price, Dec 24 2013

Tony D. Noe and Jonathan Vos Post, Primes in Fibonacci n-step and Lucas n-step Sequences, J. of Integer Sequences, Vol. 8 (2005), Article 05.4.4

Cf. A104577 (indices of prime generalized tetranacci numbers).

Cf. A000073, A001644, A092835, A105762.

A001644(a(n)) = A105762(n). - Arthur O'Dwyer, Jul 26 2024

a(37)-a(39) from Robert Price, Dec 24 2013

Name clarified by Arthur O'Dwyer, Jul 25 2024

A105285 Indices of Lucas 3-step numbers A001644 which have a nontrivial divisor in common with index.

Original entry on oeis.org

6, 15, 18, 21, 35, 39, 44, 45, 54, 55, 57, 78, 80, 84, 90, 93, 96, 117, 120, 123, 132, 133, 135, 140, 147, 154, 156, 162, 171, 174, 195, 201, 210, 213, 234, 235, 240, 245, 247, 249, 252, 259, 264, 273, 275, 279, 286, 288, 290, 291, 295, 299, 312, 318, 323, 327

Offset: 1

Jonathan Vos Post, Apr 25 2005

Extension by T. D. Noe. Wanted: closed-form formula for this as exists for Fibonacci and Lucas numbers. See also A105762 (prime Lucas 3-step numbers).

			gcd(6, A001644(6)) = gcd(6,39) = 3,
gcd(21, A001644(21)) = gcd(21,361109) = 7.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A001644, A104714, A105762.

m=300; s = LinearRecurrence[{1, 1, 1}, {3, 1, 3}, m+1]; Select[Range[m], !CoprimeQ[#, s[[#+1]]] &] (* Amiram Eldar, Sep 05 2019 *)

gcd(a(n), A001644(a(n))) > 1.

More terms from Amiram Eldar, Sep 05 2019

cp's OEIS Frontend

A104576 Indices of primes in A001644 (the Lucas 3-step numbers).

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