A083216 -id:A083216 - cp's OEIS frontend

A114566 Number of prime factors of A083216(n), counted with multiplicity.

4, 2, 4, 6, 3, 5, 4, 5, 2, 10, 5, 3, 3, 3, 4, 10, 5, 7, 2, 4, 5, 10, 4, 4, 2, 4, 5, 7, 3, 5, 5, 4, 3, 8, 4, 6, 4, 6, 4, 7, 5, 4, 3, 3, 4, 10, 5, 6, 4, 5, 5, 7, 3, 5, 6, 6, 4, 10, 5, 6, 7, 4, 4, 7, 5, 9, 4, 4, 5, 8, 2, 6, 6, 5, 5, 6, 4, 5, 5, 7, 3, 7, 5, 4, 6

Offset: 0

Jonathan Vos Post, Feb 15 2006

nonn

			a(0) = 4 because Wilf(0) = 20615674205555510 = 2 * 5 * 5623 * 366631232537 has 4 prime factors with multiplicity.
a(1) = 2 because Wilf(1) is semiprime, namely 3794765361567513 = 3 * 1264921787189171.
a(2) = 4 because Wilf(2) = 24410439567123023 = 823 * 1069 * 5779 * 4801151.
a(3) = 6 because Wilf(3) = 2^3 * 1039 * 4481 * 757266563 (note that the prime factor 2 is counted 3 times).
a(4) = 3 because Wilf(4) = 52615644495813559 = 983 * 2521 * 21231883913.
a(5) = 5 because Wilf(5) = 80820849424504095 = 3^2 * 5 * 43 * 41767880839537.

Alois P. Heinz, Table of n, a(n) for n = 0..336
R. L. Graham, A Fibonacci-Like Sequence of Composite Numbers, Math. Mag. 37, 1964, pp. 322-324.
D. E. Knuth, A Fibonacci-Like Sequence of Composite Numbers, Math. Mag. 63, 1990, pp. 21-25.
H. S. Wilf, Letter to the Editor, Math. Mag. 63, 1990, p. 284.
Eric Weisstein's World of Mathematics, Primefree Sequence.

Cf. A001222, A083216.

a:= n-> numtheory[bigomega]((<<0|1>, <1|1>>^n.
    <<20615674205555510, 3794765361567513>>)[1, 1]):
seq(a(n), n=0..80);  # Alois P. Heinz, Sep 20 2017

PrimeOmega[LinearRecurrence[{1,1},{20615674205555510,3794765361567513},100]] (* Paolo Xausa, Nov 07 2023 *)

A083216(n)=if(n==0, 20615674205555510, if(n==1, 3794765361567513, A083216(n-1)+A083216(n-2)));
A114566(n)=bigomega(A083216(n));
for(n=0,30, print1(A114566(n),", ")) \\ R. J. Mathar, Dec 05 2007

a(n) = Omega(A083216(n)) = A001222(A083216(n)).

a(n) > 1 for all n >= 0.

Corrected and extended by R. J. Mathar, Dec 05 2007
More terms from Alois P. Heinz, Sep 20 2017
Name edited by Michel Marcus, Nov 07 2023

A083104 Second-order linear recurrence sequence with a(n) = a(n-1) + a(n-2), with initial terms 331635635998274737472200656430763, 1510028911088401971189590305498785.

Original entry on oeis.org

331635635998274737472200656430763, 1510028911088401971189590305498785, 1841664547086676708661790961929548, 3351693458175078679851381267428333, 5193358005261755388513172229357881, 8545051463436834068364553496786214

Offset: 0

Harry J. Smith, Apr 23 2003

This is a second-order linear recurrence sequence with a(0) and a(1) coprime that does not contain any primes. It was found by Ronald Graham in 1964.

Indranil Ghosh, Table of n, a(n) for n = 0..4618
Arturas Dubickas, Aivaras Novikas and Jonas Šiurys, A binary linear recurrence sequence of composite numbers, Journal of Number Theory, Volume 130, Issue 8, August 2010, Pages 1737-1749.
R. L. Graham, A Fibonacci-Like sequence of composite numbers, Math. Mag. 37 (1964) 322-324.
D. Ismailescu and J. Son, A New Kind of Fibonacci-Like Sequence of Composite Numbers, J. Int. Seq. 17 (2014) # 14.8.2.
Tanya Khovanova, Recursive Sequences
D. E. Knuth, A Fibonacci-Like sequence of composite numbers, Math. Mag. 63 (1) (1990) 21-25
J. W. Nicol, A Fibonacci-like sequence of composite numbers, The Electronic Journal of Combinatorics, Volume 6 (1999), Research Paper #R44.
Carlos Rivera, Problem 31. Fibonacci- all composites sequence, The Prime Puzzles and Problems Connection.
Index entries for linear recurrences with constant coefficients, signature (1,1).

Cf. A000032 (Lucas numbers), A000045 (Fibonacci numbers), A083103, A083105, A083216, A082411, A221286.

LinearRecurrence[{1,1},{331635635998274737472200656430763,1510028911088401971189590305498785},7] (* Harvey P. Dale, Oct 29 2016 *)

a(n)=331635635998274737472200656430763*fibonacci(n-1)+ 1510028911088401971189590305498785*fibonacci(n) \\ Charles R Greathouse IV, Dec 18 2014

G.f.: (331635635998274737472200656430763+1178393275090127233717389649068022*x)/(1-x-x^2). - Colin Barker, Jun 19 2012

Name clarified by Robert C. Lyons, Feb 07 2025

A083105 Second-order linear recurrence sequence with a(n) = a(n-1) + a(n-2), with initial terms 62638280004239857, 49463435743205655.

Original entry on oeis.org

62638280004239857, 49463435743205655, 112101715747445512, 161565151490651167, 273666867238096679, 435232018728747846, 708898885966844525, 1144130904695592371, 1853029790662436896, 2997160695358029267, 4850190486020466163, 7847351181378495430

Offset: 0

Harry J. Smith, Apr 23 2003

a(0) = 62638280004239857, a(1) = 49463435743205655. This is a second-order linear recurrence sequence with a(0) and a(1) coprime that does not contain any primes. It was found by D. E. Knuth in 1990.

Seiichi Manyama, Table of n, a(n) for n = 0..4705
Arturas Dubickas, Aivaras Novikas and Jonas Šiurys, A binary linear recurrence sequence of composite numbers, Journal of Number Theory, Volume 130, Issue 8, August 2010, Pages 1737-1749.
R. L. Graham, A Fibonacci-Like sequence of composite numbers, Math. Mag. 37 (1964) 322-324.
D. Ismailescu and J. Son, A New Kind of Fibonacci-Like Sequence of Composite Numbers, J. Int. Seq. 17 (2014) # 14.8.2.
Tanya Khovanova, Recursive Sequences
D. E. Knuth, A Fibonacci-like sequence of composite numbers, Math. Mag. 63 (1) (1990) 21-25.
J. W. Nicol, A Fibonacci-like sequence of composite numbers, The Electronic Journal of Combinatorics, Volume 6 (1999), Research Paper #R44.
Carlos Rivera, Problem 31. Fibonacci- all composites sequence, The Prime Puzzles and Problems Connection.
Index entries for linear recurrences with constant coefficients, signature (1,1).

Cf. A000032 (Lucas numbers), A000045 (Fibonacci numbers), A083103, A083104, A083216, A082411, A221286.

a:= n-> (<<0|1>, <1|1>>^n. <<62638280004239857, 49463435743205655>>)[1, 1]:
seq(a(n), n=0..20);  # Alois P. Heinz, Sep 20 2021

LinearRecurrence[{1,1},{62638280004239857,49463435743205655},20] (* Paolo Xausa, Nov 07 2023 *)

G.f.: (62638280004239857-13174844261034202*x)/(1-x-x^2). [Colin Barker, Jun 19 2012]

Name clarified by Robert C. Lyons, Feb 07 2025

A082411 Second-order linear recurrence sequence with a(n) = a(n-1) + a(n-2), with initial terms 407389224418, 76343678551.

Original entry on oeis.org

407389224418, 76343678551, 483732902969, 560076581520, 1043809484489, 1603886066009, 2647695550498, 4251581616507, 6899277167005, 11150858783512, 18050135950517, 29200994734029, 47251130684546, 76452125418575, 123703256103121, 200155381521696, 323858637624817

Offset: 0

Harry J. Smith, Apr 23 2003

a(0) = 407389224418, a(1) = 76343678551. This is a second-order linear recurrence sequence with a(0) and a(1) coprime that does not contain any primes. It was found by John Nicol in 1999.

Alois P. Heinz, Table of n, a(n) for n = 0..1000
Arturas Dubickas, Aivaras Novikas and Jonas Šiurys, A binary linear recurrence sequence of composite numbers, Journal of Number Theory, Volume 130, Issue 8, August 2010, Pages 1737-1749.
R. L. Graham, A Fibonacci-Like sequence of composite numbers, Math. Mag. 37 (1964) 322-324.
D. Ismailescu and J. Son, A New Kind of Fibonacci-Like Sequence of Composite Numbers, J. Int. Seq. 17 (2014) # 14.8.2.
Tanya Khovanova, Recursive Sequences
D. E. Knuth, A Fibonacci-Like sequence of composite numbers, Math. Mag. 63 (1) (1990) 21-25
J. W. Nicol, A Fibonacci-like sequence of composite numbers, The Electronic Journal of Combinatorics, Volume 6 (1999), Research Paper #R44.
Herbert S. Wilf, Letters to the Editor Math. Mag. 63, 284, 1990.
Index entries for linear recurrences with constant coefficients, signature (1,1).

Cf. A000032 (Lucas numbers), A000045 (Fibonacci numbers), A083103, A083104, A083105, A083216, A221286.

a:= n-> (<<0|1>, <1|1>>^n. <<407389224418, 76343678551>>)[1, 1]:
seq(a(n), n=0..20);  # Alois P. Heinz, Apr 04 2013

LinearRecurrence[{1,1},{407389224418,76343678551},25] (* Paolo Xausa, Nov 07 2023 *)

G.f.: (407389224418-331045545867*x)/(1-x-x^2). [Colin Barker, Jun 19 2012]

Name clarified by Robert C. Lyons, Feb 07 2025

A221286 Vsemirnov's sequence.

Original entry on oeis.org

106276436867, 35256392432, 141532829299, 176789221731, 318322051030, 495111272761, 813433323791, 1308544596552, 2121977920343, 3430522516895, 5552500437238, 8983022954133, 14535523391371, 23518546345504, 38054069736875, 61572616082379, 99626685819254, 161199301901633, 260825987720887, 422025289622520

Offset: 0

Charles R Greathouse IV, Feb 05 2013

A primefree linear recurrence with no common factors. As of 2004 no such sequences with smaller starting terms were known.

Seiichi Manyama, Table of n, a(n) for n = 0..4733 (terms 0..1000 from Alois P. Heinz)
Arturas Dubickas, Aivaras Novikas, and Jonas Šiurys, A binary linear recurrence sequence of composite numbers, Journal of Number Theory, Volume 130, Issue 8, August 2010, Pages 1737-1749.
D. Ismailescu and J. Son, A New Kind of Fibonacci-Like Sequence of Composite Numbers, J. Int. Seq. 17 (2014) # 14.8.2.
Maxim Vsemirnov, A new Fibonacci-like sequence of composite numbers, Journal of Integer Sequences 7:3 (2004).
Index entries for linear recurrences with constant coefficients, signature (1,1).

Other primefree linear recurrences: A083104 (Graham 1964), A082411 (Nicol 1999), A083105 (Knuth 1990), A083216 (Wilf 1990).

a:= n-> (<<0|1>, <1|1>>^n. <<106276436867, 35256392432>>)[1, 1]:
seq(a(n), n=0..20);  # Alois P. Heinz, Apr 04 2013

LinearRecurrence[{1, 1}, {106276436867, 35256392432}, 20] (* Alonso del Arte, Feb 05 2013 *)

Vec((106276436867-71020044435*x)/(1-x-x^2)+O(x^30)) \\ Charles R Greathouse IV, Dec 09 2014

a(n) = a(n-1) + a(n-2).

G.f.: (106276436867-71020044435*x)/(1-x-x^2).

Offset corrected by Alois P. Heinz, Apr 04 2013

A083086 a(n) = (2^(n+1) + (-4)^n)/3.

Original entry on oeis.org

1, 0, 8, -16, 96, -320, 1408, -5376, 22016, -87040, 350208, -1396736, 5595136, -22364160, 89489408, -357892096, 1431699456, -5726535680, 22906667008, -91625619456, 366504574976, -1466014105600, 5864064811008, -23456242466816, 93825003421696, -375299946577920

Offset: 0

Paul Barry, Apr 23 2003

Binomial transform of A083085.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (-2,8).

Cf. A000079, A078008, A083085, A083216.

[(2*2^n+(-4)^n)/3: n in [0..30]]; // Vincenzo Librandi, Nov 12 2011

LinearRecurrence[{-2,8}, {1,0}, 41] (* G. C. Greubel, Feb 19 2023 *)

a(n)=(2*2^n+(-4)^n)/3 \\ Charles R Greathouse IV, Oct 07 2015

[(2^(n+1)+(-4)^n)/3 for n in range(41)] # G. C. Greubel, Feb 19 2023

a(n) = (2*2^n + (-4)^n)/3.
G.f.: (1+2*x)/((1+4*x)*(1-2*x)).
E.g.f.: (2*exp(2*x) + exp(-4*x))/3.
a(n) = (-1)^n*A000079(n)*A078008(n). - Paul Barry, Feb 12 2004
a(n) = -2*a(n-1) + 8*a(n-2). - Vincenzo Librandi, Nov 12 2011

A347904 Array read by antidiagonals, m, n >= 1: T(m,n) is the first prime (after the two initial terms) in the Fibonacci-like sequence with initial terms m and n, or 0 if no such prime exists.

Original entry on oeis.org

2, 3, 3, 7, 0, 5, 5, 5, 5, 5, 11, 0, 0, 0, 7, 7, 7, 7, 7, 7, 7, 23, 0, 13, 0, 11, 0, 17, 17, 41, 0, 23, 13, 0, 11, 19, 19, 0, 17, 0, 0, 0, 13, 0, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 23, 0, 0, 0, 19, 0, 17, 0, 0, 0, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13

Offset: 1

Pontus von Brömssen, Sep 18 2021

There are cases where T(m,n) = 0 even when m and n are coprime; see A082411, A083104, A083105, A083216, and A221286. The smallest (in the sense that m+n is as small as possible) known case where this occurs appears to be m = 106276436867, n = 35256392432 (Vsemirnov's sequence, A221286).

			Array begins:
  m\n|  1  2  3  4  5  6  7  8  9 10  11 12  13  14 15 16
  ---+---------------------------------------------------
   1 |  2  3  7  5 11  7 23 17 19 11  23 13  41  29 31 17
   2 |  3  0  5  0  7  0 41  0 11  0  13  0  43   0 17  0
   3 |  5  5  0  7 13  0 17 11  0 13 103  0  29  17  0 19
   4 |  5  0  7  0 23  0 11  0 13  0  41  0  17   0 19  0
   5 |  7  7 11 13  0 11 19 13 23  0  43 17  31  19  0 37
   6 |  7  0  0  0 11  0 13  0  0  0  17  0  19   0  0  0
   7 | 17 11 13 11 17 13  0 23 41 17  29 19  53   0 37 23
   8 | 19  0 11  0 13  0 37  0 17  0  19  0  89   0 23  0
   9 | 11 11  0 13 19  0 23 17  0 19  31  0 149  23  0 41
  10 | 11  0 13  0  0  0 17  0 19  0  53  0  23   0  0  0
  11 | 13 13 17 19 37 17 43 19 29 31   0 23  37 103 41 43
  12 | 13  0  0  0 17  0 19  0  0  0  23  0 101   0  0  0
  13 | 29 17 19 17 23 19 47 29 31 23  59 37   0  41 43 29
  14 | 31  0 17  0 19  0  0  0 23  0  61  0  67   0 29  0
  15 | 17 17  0 19  0  0 29 23  0  0  37  0  41  29  0 31
  16 | 17  0 19  0 47  0 23  0 59  0 103  0  29   0 31  0
T(2,7) = 41, because the first prime in A022113, excluding the two initial terms, is 41.

Cf. A022113, A082411, A083104, A083105, A083216, A221286, A347905.

# Note that in the (rare) case when m and n are coprime but there are no primes in the Fibonacci-like sequence, this function will go into an infinite loop.
from sympy import isprime,gcd
def A347904(m,n):
    if gcd(m,n) != 1:
        return 0
    m,n = n,m+n
    while not isprime(n):
        m,n = n,m+n
    return n

T(m,n) = 0 if m and n have a common factor.

T(m,n) = T(n,m+n) if m+n is not prime, otherwise T(m,n) = m+n.

A347905 Array read by antidiagonals, m, n >= 1: T(m,n) is the position of the first prime (after the two initial terms) in the Fibonacci-like sequence with initial terms m and n, or 0 if no such prime exists.

Original entry on oeis.org

2, 2, 2, 3, 0, 3, 2, 2, 2, 2, 3, 0, 0, 0, 3, 2, 2, 2, 2, 2, 2, 4, 0, 3, 0, 3, 0, 4, 3, 5, 0, 4, 3, 0, 3, 4, 3, 0, 3, 0, 0, 0, 3, 0, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 0, 0, 0, 3, 0, 3, 0, 0, 0, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 0, 6, 0, 3, 0, 0, 0, 3, 0, 3, 0, 4

Offset: 1

Pontus von Brömssen, Sep 18 2021

There are cases where T(m,n) = 0 even when m and n are coprime; see A082411, A083104, A083105, A083216, and A221286.

The largest value of T(m,n) for m, n <= 5000 is T(1591,300) = 17262.

			Array begins:
  m\n|  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20
  ---+------------------------------------------------------------
   1 |  2  2  3  2  3  2  4  3  3  2  3  2  4  3  3  2  4  2  4  3
   2 |  2  0  2  0  2  0  5  0  2  0  2  0  4  0  2  0  2  0  4  0
   3 |  3  2  0  2  3  0  3  2  0  2  6  0  3  2  0  2  3  0  3  2
   4 |  2  0  2  0  4  0  2  0  2  0  4  0  2  0  2  0  4  0  2  0
   5 |  3  2  3  3  0  2  3  2  3  0  4  2  3  2  0  3  4  2  3  0
   6 |  2  0  0  0  2  0  2  0  0  0  2  0  2  0  0  0  2  0  5  0
   7 |  4  3  3  2  3  2  0  3  4  2  3  2  4  0  3  2  3  3  4  3
   8 |  4  0  2  0  2  0  4  0  2  0  2  0  5  0  2  0  4  0  4  0
   9 |  3  2  0  2  3  0  3  2  0  2  3  0  6  2  0  3  3  0  3  2
  10 |  2  0  2  0  0  0  2  0  2  0  4  0  2  0  0  0  4  0  2  0
  11 |  3  2  3  3  4  2  4  2  3  3  0  2  3  5  3  3  4  2  4  2
  12 |  2  0  0  0  2  0  2  0  0  0  2  0  5  0  0  0  2  0  2  0
  13 |  4  3  3  2  3  2  4  3  3  2  4  3  0  3  3  2  3  2  4  3
  14 |  4  0  2  0  2  0  0  0  2  0  4  0  4  0  2  0  2  0  5  0
  15 |  3  2  0  2  0  0  3  2  0  0  3  0  3  2  0  2  6  0  3  0
  16 |  2  0  2  0  4  0  2  0  4  0  5  0  2  0  2  0  4  0  4  0
  17 |  3  2  3  5 10  2  3  6  4  3  4  2  3  2  3  5  0  3  7  2
  18 |  2  0  0  0  2  0  5  0  0  0  2  0  2  0  0  0  5  0  2  0
  19 |  4  3  4  2  3  3  4  5  3  2  3  2  6  3  4  5  3  2  0  3
  20 |  4  0  2  0  0  0  4  0  2  0  2  0  4  0  0  0  2  0  4  0
T(2,7) = 5, because 5 is the smallest k >= 2 for which A022113(k) is prime.

Cf. A022113, A082411, A083104, A083105, A083216, A221286, A347904.

# Note that in the (rare) case when m and n are coprime but there are no primes in the Fibonacci-like sequence, this function will go into an infinite loop.
from sympy import isprime,gcd
def A347905(m,n):
    if gcd(m,n) != 1:
        return 0
    m,n = n,m+n
    k=2
    while not isprime(n):
        m,n = n,m+n
        k += 1
    return k

T(m,n) = 0 if m and n have a common factor.

T(m,n) = T(n,m+n) + 1 if m+n is not prime, otherwise T(m,n) = 2.

A108156 Numbers n such that a(n) is prime, where a(n) = a(n-1) + a(n-2), a(1) = 3794765361567513, a(2) = 20615674205555510.

Original entry on oeis.org

138, 163, 190, 523, 1855, 3228, 3579, 6468, 7170, 10230, 12783, 17259, 60139, 91315, 97923, 101823, 156075

Offset: 1

Alonso del Arte, Jun 06 2005

nonn

In his biography of Paul Erdős, Hoffman cited Wilf's Fibonacci-like primefree sequence (A083216). But, as Weisstein points out, Hoffman inadvertently switched the two initial terms, resulting in a sequence that appears primefree for the first 137 terms. Term 138 is 439351292910452432574786963588089477522344721, which is prime. The first Mathematica program below comes from Weisstein's Mathematica notebook.

Paul Hoffman. The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical Truth. New York: Hyperion, 1998.

Eric Weisstein's World of Mathematics, Primefree Sequence.
Herbert S. Wilf, Letters to the Editor Math. Mag. 63, 284, 1990.

Cf. A083216.

a[1] := 3794765361567513; a[2] := 20615674205555510; a[n_] := a[n] = a[n - 2] + a[n - 1]; Flatten[Position[Table[a[n], {n, 10^4}], ?PrimeQ]] (* _Eric W. Weisstein *)
Flatten[Position[LinearRecurrence[{1,1},{3794765361567513,20615674205555510},160000],?PrimeQ]] (* _Harvey P. Dale, Nov 29 2011 *)

a(10)-a(12) from Robert G. Wilson v, Jun 07 2005
a(13) from Eric W. Weisstein, Sep 23 2005
a(14) from Eric W. Weisstein, Oct 06 2005
a(15)-a(16) from Eric W. Weisstein, Oct 10 2005
a(17) from Eric W. Weisstein, Nov 09 2005
Definition adapted to offset by Georg Fischer, Jun 18 2021

A348204 Fibonacci-like sequence of composite numbers with a(0) = 759135467284, a(1) = 74074527465.

Original entry on oeis.org

759135467284, 74074527465, 833209994749, 907284522214, 1740494516963, 2647779039177, 4388273556140, 7036052595317, 11424326151457, 18460378746774, 29884704898231, 48345083645005, 78229788543236, 126574872188241, 204804660731477, 331379532919718, 536184193651195

Offset: 0

Chittaranjan Pardeshi, Oct 06 2021

This is a second-order linear recurrence sequence with a(0) and a(1) coprime that does not contain any primes.

This sequence was found using Knuth's method.

R. L. Graham, A Fibonacci-Like sequence of composite numbers, Math. Mag., Vol. 37, No. 5 (1964), pp. 322-324.
Donald E. Knuth, A Fibonacci-Like sequence of composite numbers, Math. Mag., Vol. 63, No. 1 (1990), pp. 21-25.
Index entries for linear recurrences with constant coefficients, signature (1,1).

Cf. A221286, A083104, A082411, A083105, A083216, A083216.

a:= n-> (<<0|1>, <1|1>>^n. <<759135467284, 74074527465>>)[1, 1]:
seq(a(n), n=0..16);  # Alois P. Heinz, Oct 06 2021

LinearRecurrence[{1, 1}, {759135467284, 74074527465}, 17] (* Amiram Eldar, Oct 07 2021 *)

a(n)=759135467284*fibonacci(n-1)+ 74074527465*fibonacci(n)

a(n) = a(n-1) + a(n-2).

cp's OEIS Frontend

A114566 Number of prime factors of A083216(n), counted with multiplicity.

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A083104 Second-order linear recurrence sequence with a(n) = a(n-1) + a(n-2), with initial terms 331635635998274737472200656430763, 1510028911088401971189590305498785.

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A083105 Second-order linear recurrence sequence with a(n) = a(n-1) + a(n-2), with initial terms 62638280004239857, 49463435743205655.

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A082411 Second-order linear recurrence sequence with a(n) = a(n-1) + a(n-2), with initial terms 407389224418, 76343678551.

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A221286 Vsemirnov's sequence.

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A083086 a(n) = (2^(n+1) + (-4)^n)/3.

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A347904 Array read by antidiagonals, m, n >= 1: T(m,n) is the first prime (after the two initial terms) in the Fibonacci-like sequence with initial terms m and n, or 0 if no such prime exists.

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