A084662 -id:A084662 - cp's OEIS frontend

A134734 First differences of A084662.

2, 3, 1, 5, 3, 1, 1, 1, 1, 11, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 23, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 47, 3, 1, 5, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 101, 3, 1, 1

Offset: 1

N. J. A. Sloane, Jan 28 2008

nonn

Eric S. Rowland, A simple prime-generating recurrence, Abstracts Amer. Math. Soc., 29 (No. 1, 2008), p. 50 (Abstract 1035-11-986).

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Eric S. Rowland, A simple prime-generating recurrence, arXiv:0710.3217 [math.NT], 2007-2008.

See A106108 for other cross-references.

Cf. A132199, A134743, A134744.

a134734 n = a134734_list !! (n-1)
a134734_list = zipWith (-) (tail a084662_list) a084662_list
-- Reinhard Zumkeller, Nov 15 2013

b[1] = 4; b[n_] := b[n] = b[n-1] + GCD[n, b[n-1]];
Table[b[n], {n, 104}] // Differences (* Jean-François Alcover, Sep 28 2018 *)

a(n) = A132199(n), n > 2. - R. J. Mathar, Mar 28 2012

A106108 Rowland's prime-generating sequence: a(1) = 7; for n > 1, a(n) = a(n-1) + gcd(n, a(n-1)).

Original entry on oeis.org

7, 8, 9, 10, 15, 18, 19, 20, 21, 22, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 69, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 141, 144, 145, 150, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168

Offset: 1

N. J. A. Sloane, Jan 28 2008

nonn

The title refers to the sequence of first differences, A132199.
Setting a(1) = 4 gives A084662.
Rowland proves that the first differences are all 1's or primes. The prime differences form A137613.
See A137613 for additional comments, links and references. - Jonathan Sondow, Aug 14 2008
Not all starting values generate differences of all 1's or primes. The following a(1) generate composite differences: 532, 533, 534, 535, 698, 699, 706, 707, 708, 709, 712, 713, 714, 715, ... - Dmitry Kamenetsky, Jul 18 2015
The same results are obtained if 2's are removed from n when gcd is performed, so the following is also true: a(1) = 7; for n > 1, a(n) = a(n-1) + gcd(A000265(n), a(n-1)). - David Morales Marciel, Sep 14 2016

Eric S. Rowland, A simple prime-generating recurrence, Abstracts Amer. Math. Soc., 29 (No. 1, 2008), p. 50 (Abstract 1035-11-986).

Indranil Ghosh, Table of n, a(n) for n = 1..25000 (terms 1..1000 from T. D. Noe)
Fernando Chamizo, Dulcinea Raboso and Serafin Ruiz-Cabello, On Rowland's sequence, Electronic J. Combin., Vol. 18(2), 2011, #P10.
Brian Hayes, Pumping the Primes, bit-player, 19 August 2015.
Eric S. Rowland, A simple prime-generating recurrence, arXiv:0710.3217 [math.NT], 2007-2008.
Eric S. Rowland, Prime-Generating Recurrence, Wolfram Demonstrations Project. - _Robert G. Wilson v_, Sep 10 2008
Eric S. Rowland, Prime-Generating Recurrences and a Tale of Logarithmic Scale, YouTube video, 2023.

Cf. A084662, A084663, A132199, A134734, A134736, A134743, A134744, A134162, A137613, A221869.

Cf. A230504.

a106108 n = a106108_list !! (n-1)
a106108_list =
   7 : zipWith (+) a106108_list (zipWith gcd a106108_list [2..])
-- Reinhard Zumkeller, Nov 15 2013

[n le 1 select 7 else Self(n-1) + Gcd(n, Self(n-1)): n in [1..70]]; // Vincenzo Librandi, Jul 19 2015

S:=7; f:= proc(n) option remember; global S; if n=1 then RETURN(S); else RETURN(f(n-1)+gcd(n,f(n-1))); fi; end; [seq(f(n),n=1..200)];

a[1] = 7; a[n_] := a[n] = a[n - 1] + GCD[n, a[n - 1]]; Array[a, 66] (* Robert G. Wilson v, Sep 10 2008 *)

a=vector(100);a[1]=7;for(n=2,#a,a[n]=a[n-1]+gcd(n,a[n-1]));a \\ Charles R Greathouse IV, Jul 15 2011

from itertools import count, islice
from math import gcd
def A106108_gen(): # generator of terms
    yield (a:=7)
    for n in count(2):
        yield (a:=a+gcd(a,n))
A106108_list = list(islice(A106108_gen(),20)) # Chai Wah Wu, Mar 14 2023

A084663 a(1) = 8; a(n) = a(n-1) + gcd(a(n-1), n).

Original entry on oeis.org

8, 10, 11, 12, 13, 14, 21, 22, 23, 24, 25, 26, 39, 40, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 87, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 177, 180, 181, 182, 189, 190

Offset: 1

Matthew Frank (mfrank(AT)wopr.wolfram.com) on behalf of the 2003 New Kind of Science Summer School, Jul 15 2003

nonn

The first 150000000 differences are all primes or 1. Is this true in general?

The proof of the conjecture is identical to the proof in the Rowland link. - Yifan Xie, Apr 11 2025

Eric S. Rowland, A simple prime-generating recurrence, Abstracts Amer. Math. Soc., 29 (No. 1, 2008), p. 50 (Abstract 1035-11-986).

Indranil Ghosh, Table of n, a(n) for n = 1..50000
Eric S. Rowland, A natural prime-generating recurrence, arXiv:0710.3217 [math.NT], 2007-2008.
Eric S. Rowland, A natural prime-generating recurrence, JIS 11 (2008) 08.2.8.

Cf. A084662, A106108.

Cf. A230504, A134744 (first differences), A134736.

a084663 n = a084663_list !! (n-1)
a084663_list =
   8 : zipWith (+) a084663_list (zipWith gcd a084663_list [2..])
-- Reinhard Zumkeller, Nov 15 2013

S := 8; f := proc(n) option remember; global S; if n=1 then S else f(n-1)+igcd(n,f(n-1)); fi; end;

a[n_]:= a[n]= If[n==1,8, a[n-1] + GCD[n, a[n-1]]]; Table[a[n], {n,70}]
RecurrenceTable[{a[1]==8,a[n]==a[n-1]+GCD[a[n-1],n]},a,{n,70}] (* Harvey P. Dale, Apr 12 2016 *)

@CachedFunction
def a(n): # a = A084663
    if (n==1): return 8
    else: return a(n-1) + gcd(a(n-1), n)
[a(n) for n in range(1, 71)] # G. C. Greubel, Mar 22 2023

A134162 Let S(k) be the sequence s() defined by s(1) = k; for i > 1, s(i) = s(i-1) + gcd(s(i-1), i). Start with the list of positive integers and remove any k's for which S(k) merges with an S(m) with m < k. Each value k > 1 is conjectural.

Original entry on oeis.org

1, 2, 4, 8, 16, 20, 44, 92, 110, 136, 152, 170, 172, 188, 200, 212, 236, 242, 256, 272, 316, 332, 368, 440, 488, 500, 590, 616, 620, 632, 650, 676, 704, 710, 742, 788, 824, 848, 892, 946, 952, 968, 1010, 1034, 1036, 1052, 1058, 1088, 1118

Offset: 1

Eric Rowland, Jan 29 2008

nonn

For the given initial values k, it is conjectural that their sequences S(k) never merge. The S(k) have been checked to be distinct for 2^60 terms (see Rowland link), but it is possible that they merge later on.

			From _Danny Rorabaugh_, Apr 02 2015: (Start)
S(1) = A000027 is the positive integers.
S(2) = [2,4,5,...,i+2,...].
S(3) = [3,4,5,...,i+2,...] merges with S(2) at index 2.
S(4) = [4,6,9,10,15,18,19,20,21,22,33,...] = A084662.
S(5) = [5,6,9,...] = A134736 merges with S(4) at index 2.
(End)

Eric Rowland, A Natural Prime-Generating Recurrence (Section 5: Primes), Journal of Integer Sequences, Vol. 11 (2008), Article 08.2.8.

Cf. A000027 (S(1)), A084662 (S(4)), A134736 (S(5)), A106108 (S(7)), A084663 (S(8)).

Cf. A106108 for other Crossrefs.

A166945 Records of first differences of A166944.

Original entry on oeis.org

2, 3, 7, 13, 43, 139, 313, 661, 1321, 2659, 5419, 10891, 22039, 44383, 88801, 177841, 355723, 713833, 1427749, 2860771, 5725453, 11461141, 22933441, 45895573, 91793059, 183616423, 367232911, 734482123, 1468965061, 2937930211, 5875882249, 11751795061, 23503590559, 47007181621, 94014363763

Offset: 1

Vladimir Shevelev, Oct 24 2009, Nov 05 2009

nonn

Conjecture. Each term of the sequence is the greater of a pair of twin primes (A006512).

E. S. Rowland, A natural prime-generating recurrence, Journal of Integer Sequences, Vol.11(2008), Article 08.2.8. arXiv:0710.3217 [math.NT]
V. Shevelev, An infinite set of generators of primes based on the Rowland idea and conjectures concerning twin primes, arXiv:0910.4676 [math.NT], 2009.
V. Shevelev, Three theorems on twin primes, arXiv:0911.5478 [math.NT], 2009-2010.

Cf. A166944, A084662, A084663, A106108, A132199, A134162, A135506, A135508, A118679, A120293.

Reap[Print[old = r = 2]; Sow[old]; For[n = 2, n <= 10^6, n++, d = GCD[old, If[OddQ[n], n-2, n]]; If[d>r, r=d; Print[d]; Sow[d]]; old += d]][[2, 1]] (* Jean-François Alcover, Nov 03 2018, from PARI *)

print1(old=r=2); for(n=2,1e11, d=gcd(old,if(n%2,n-2,n)); if(d>r, r=d; print1(", "d)); old+=d) \\ Charles R Greathouse IV, Oct 13 2017

6 more terms from R. J. Mathar, Nov 19 2009; extension beginning with a(19) from Benoit Cloitre (private communication to Vladimir Shevelev)
a(25), a(26) from D. S. McNeil, Dec 13 2010
a(27)-a(30) from Charles R Greathouse IV, Oct 13 2017
a(31)-a(35) from Charles R Greathouse IV, Oct 17 2017

A166944 a(1)=2; a(n) = a(n-1) + gcd(n, a(n-1)) if n is even, a(n) = a(n-1) + gcd(n-2, a(n-1)) if n is odd.

Original entry on oeis.org

2, 4, 5, 6, 9, 12, 13, 14, 21, 22, 23, 24, 25, 26, 39, 40, 45, 54, 55, 60, 61, 62, 63, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 129, 130, 135, 138, 139, 140, 147, 148, 149, 150, 151, 152, 153, 154, 155, 160, 161, 162, 163

Offset: 1

Vladimir Shevelev, Oct 24 2009

nonn

Conjecture: Every record of differences a(n)-a(n-1) more than 5 is the greater of twin primes (A006512).

Harvey P. Dale, Table of n, a(n) for n = 1..1000
E. S. Rowland, A natural prime-generating recurrence, Journal of Integer Sequences, Vol.11(2008), Article 08.2.8. arXiv:0710.3217 [math.NT]
V. Shevelev, An infinite set of generators of primes based on the Rowland idea and conjectures concerning twin primes, arXiv:0910.4676 [math.NT], 2009. - _Vladimir Shevelev_, Oct 27 2009
V. Shevelev, Three theorems on twin primes, arXiv:0911.5478 [math.NT], 2009-2010. - _Vladimir Shevelev_, Dec 03 2009

Cf. A084662, A084663, A106108, A132199, A134162, A135506, A135508, A118679, A120293.

A166944 := proc(n) option remember; if n = 1 then 2; else p := procname(n-1) ; if type(n,'even') then p+igcd(n,p) ; else p+igcd(n-2,p) ; end if; end if; end proc: # R. J. Mathar, Sep 03 2011

nxt[{n_,a_}]:={n+1,If[OddQ[n],a+GCD[n+1,a],a+GCD[n-1,a]]}; Transpose[ NestList[ nxt,{1,2},70]][[2]] (* Harvey P. Dale, Feb 10 2015 *)

print1(a=2); for(n=2, 100, d=gcd(a, if(n%2, n-2, n)); print1(", "a+=d)) \\ Charles R Greathouse IV, Oct 13 2017

Terms beginning with a(18) corrected by Vladimir Shevelev, Nov 10 2009

A137613 Omit the 1's from Rowland's sequence f(n) - f(n-1) = gcd(n,f(n-1)), where f(1) = 7.

Original entry on oeis.org

5, 3, 11, 3, 23, 3, 47, 3, 5, 3, 101, 3, 7, 11, 3, 13, 233, 3, 467, 3, 5, 3, 941, 3, 7, 1889, 3, 3779, 3, 7559, 3, 13, 15131, 3, 53, 3, 7, 30323, 3, 60647, 3, 5, 3, 101, 3, 121403, 3, 242807, 3, 5, 3, 19, 7, 5, 3, 47, 3, 37, 5, 3, 17, 3, 199, 53, 3, 29, 3, 486041, 3, 7, 421, 23

Offset: 1

Jonathan Sondow, Jan 29 2008, Jan 30 2008

nonn

Rowland proves that each term is prime. He says it is likely that all odd primes occur.
In the first 5000 terms, there are 965 distinct primes and 397 is the least odd prime that does not appear. - T. D. Noe, Mar 01 2008
In the first 10000 terms, the least odd prime that does not appear is 587, according to Rowland. - Jonathan Sondow, Aug 14 2008
Removing duplicates from this sequence yields A221869. The duplicates are A225487. - Jonathan Sondow, May 03 2013

			f(n) = 7, 8, 9, 10, 15, 18, 19, 20, ..., so f(n) - f(n-1) = 1, 1, 1, 5, 3, 1, 1, ... and a(n) = 5, 3, ... .
From _Vladimir Shevelev_, Mar 03 2010: (Start)
  a(1) = Lpf(6-1) = 5;
  a(2) = Lpf(6-2+5) = 3;
  a(3) = Lpf(6-3+5+3) = 11;
  a(4) = Lpf(6-4+5+3+11) = 3;
  a(5) = Lpf(6-5+5+3+11+3) = 23. (End)

T. D. Noe, Table of n, a(n) for n = 1..5000
Jean-Paul Delahaye, Déconcertantes conjectures, Pour la science, 5 (2008), 92-97.
Brian Hayes, Pumping the Primes, bit-player, 19 August 2015.
John Moyer, Source code in C and C++ to print this sequence or sorted and unique values from this sequence. [From John Moyer (jrm(AT)rsok.com), Nov 06 2009]
Ivars Peterson, A New Formula for Generating Primes, The Mathematical Tourist.
Eric S. Rowland, A simple prime-generating recurrence, Abstracts Amer. Math. Soc. 29 (No. 1, 2008), p. 50 (Abstract 1035-11-986).
Eric S. Rowland, A natural prime-generating recurrence, arXiv:0710.3217 [math.NT], 2007-2008.
Eric S. Rowland, A natural prime-generating recurrence, J. of Integer Sequences 11 (2008), Article 08.2.8.
Eric Rowland, A simple recurrence that produces complex behavior ..., A New Kind of Science blog.
Eric Rowland, Prime-Generating Recurrence, Wolfram Demonstrations Project, 2008.
Eric Rowland, A Bizarre Way to Generate Primes, YouTube video, 2023.
Jeffrey Shallit, Rutgers Graduate Student Finds New Prime-Generating Formula, Recursivity blog.
Vladimir Shevelev, Generalizations of the Rowland theorem, arXiv:0911.3491 [math.NT], 2009-2010.
Wikipedia, Formula for primes.

f(n) = f(n-1) + gcd(n, f(n-1)) = A106108(n) and f(n) - f(n-1) = A132199(n-1).
Cf. also A084662, A084663, A134734, A134736, A134743, A134744, A221869.
Cf. A020639, A168008, A190894, A231900.

a137613 n = a137613_list !! (n-1)
a137613_list =  filter (> 1) a132199_list
-- Reinhard Zumkeller, Nov 15 2013

A137613_list := proc(n)
local a, c, k, L;
L := NULL; a := 7;
for k from 2 to n do
    c := igcd(k,a);
    a := a + c;
    if c > 1 then L:=L,c fi;
od;
L end:
A137613_list(500000); # Peter Luschny, Nov 17 2011

f[1] = 7; f[n_] := f[n] = f[n - 1] + GCD[n, f[n - 1]]; DeleteCases[Differences[Table[f[n], {n, 10^6}]], 1] (* Alonso del Arte, Nov 17 2011 *)

ub=1000; n=3; a=9; while(nDaniel Constantin Mayer, Aug 31 2014

from itertools import count, islice
from math import gcd
def A137613_gen(): # generator of terms
    a = 7
    for n in count(2):
        if (b:=gcd(a,n)) > 1: yield b
        a += b
A137613_list = list(islice(A137613_gen(),20)) # Chai Wah Wu, Mar 14 2023

Denote by Lpf(n) the least prime factor of n. Then a(n) = Lpf( 6-n+Sum_{i=1..n-1} a(i) ). - Vladimir Shevelev, Mar 03 2010
a(n) = A168008(2*n+4) (conjectured). - Jon Maiga, May 20 2021
a(n) = A020639(A190894(n)). - Seiichi Manyama, Aug 11 2023

A167053 a(1)=3; for n > 1, a(n) = 1 + a(n-1) + gcd( a(n-1)*(a(n-1)+2), A073829(a(n-1)) ).

Original entry on oeis.org

3, 19, 39, 81, 165, 333, 335, 673, 1347, 1349, 1351, 1353, 1355, 1357, 1359, 2721, 2723, 2725, 2727, 5457, 5459, 5461, 5463, 5465, 5467, 5469, 10941, 10943, 10945, 10947, 21897, 21899, 21901, 21903, 21905, 21907, 21909, 43821, 43823, 43825, 43827, 43829, 43831

Offset: 1

Vladimir Shevelev, Oct 27 2009

nonn

The first differences are 16, 20, 42, etc. They are either 2 or in A075369 or in A008864, see A167054.

A proof follows from Clement's criterion of twin primes.

			a(2) = 1 + 3 + gcd(3*5, 4*(2! + 1) + 3) = 19.

E. Trost, Primzahlen, Birkhäuser-Verlag, 1953, pages 30-31.

Amiram Eldar, Table of n, a(n) for n = 1..206
P. A. Clement, Congruences for sets of primes, Amer. Math. Monthly, 56 (1949), 23-25.

Cf. A073829, A008864, A167054.

Cf. A166944, A166945, A116533, A163961, A163963, A084662, A084663, A106108, A132199, A134162, A135506, A135508, A118679, A120293.

A073829 := proc(n) n+4*((n-1)!+1) ; end proc:
A167053 := proc(n) option remember ; local aprev; if n = 1 then 3; else aprev := procname(n-1) ; 1+aprev+gcd(aprev*(aprev+2),A073829(aprev)) ; end if; end proc:
seq(A167053(n),n=1..60) ; # R. J. Mathar, Dec 17 2009

A073829[n_] := 4((n-1)! + 1) + n;
a[1] = 3;
a[n_] := a[n] = 1 + a[n-1] + GCD[a[n-1] (a[n-1] + 2), A073829[a[n-1]]];
Array[a, 60] (* Jean-François Alcover, Mar 25 2020 *)

Definition shortened and values from a(4) on replaced by R. J. Mathar, Dec 17 2009

A167168 Sequence of prime gaps which characterize Rowland sequences of prime-generating recurrences.

Original entry on oeis.org

3, 7, 17, 19, 31, 43, 53, 67, 71, 79, 97, 103, 109, 113, 127, 137, 151, 163, 173, 181, 191, 197, 199, 211, 229, 239, 241, 251, 257, 269, 271, 283, 293, 317, 331, 337, 349, 367, 373

Offset: 1

Vladimir Shevelev, Oct 29 2009

nonn

Consider the Rowland sequences with recurrence N(n)= N(n-1)+gcd(n,N(n-1)).
For some of these, like the prototypical A106108, the first differences N(n)-N(n-1) are always 1 or primes.
If for some position p (a prime) N(p-1)=2*p, then the arXiv preprint shows that N is indeed in that class of prime-generating sequences.
Since then N(p)=N(p-1)+p, the prime p characterizes at the same time the gap (first difference) and location in the sequence.
In the same sequence at some larger value of p, we may again have N(p-1)=2*p. In these cases, we put all these p's satisfying that equation into a generator class.
For each of the generator classes, the OEIS sequence shows the smallest member (prime) in that class. So this is a trace of how many essentially different sequences with this N(p-1)=2*p property exist.

			We put a(1)=3 since the N-sequence 4, 6, 9, 10, 15, 18, 19, 20.. = A084662 (essentially the same as A106108) has a first difference of p=3 at position p-1=2, N(2)=2*3.
It has a first difference of p=5 at p-1=4, a first difference of p=11 at p=10, so we put {3,5,11,23,..} into that class. This leaves p=7=a(2) as the lowest prime to be covered by the next class. This is first realized by N = 8, 10, 11, 12, 13, 14, 21, 22, 23, 24, 25, 26, 39.. = A084663. Here N(12)=2*13, so p=13 is in the same class as p=7, namely {7,13,29,59,131,..}. This leaves p=17=a(3) to be the smallest member in a new class, namely {17,41,83,167,..}.

E. S. Rowland, A natural prime-generating recurrence, Journal of Integer Sequences, Vol. 11 (2008), Article 08.2.8
V. Shevelev, A new generator of primes based on the Rowland idea, arXiv:0910.4676 [math.NT], 2009.

Cf. A106108, A167053, A116533, A163963, A084662, A084663, A134162.

Edited, a(1) set to 3, 37 replaced by 31, and extended beyond 53 by R. J. Mathar, Dec 17 2009

A167054 Values of A167053(k)-A167053(k-1)-1 not equal to 1.

Original entry on oeis.org

15, 19, 41, 83, 167, 337, 673, 1361, 2729, 5471, 10949, 21911, 43853, 87719, 175447, 350899, 701819, 1403641, 2807303, 5614657, 11229331, 22458671, 44917381, 89834777, 179669557, 359339171, 718678369

Offset: 1

Vladimir Shevelev, Oct 27 2009

All terms of the sequence are primes or products of twin primes (A037074).

Cf. A167053, A166944, A166945, A116533, A163961, A163963, A084662, A084663, A106108, A132199, A134162, A135506, A135508, A118679, A120293

Values from a(3) on replaced by R. J. Mathar, Dec 17 2009

More terms from Amiram Eldar, Sep 13 2019

cp's OEIS Frontend

A134734 First differences of A084662.

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A106108 Rowland's prime-generating sequence: a(1) = 7; for n > 1, a(n) = a(n-1) + gcd(n, a(n-1)).

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A084663 a(1) = 8; a(n) = a(n-1) + gcd(a(n-1), n).

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A134162 Let S(k) be the sequence s() defined by s(1) = k; for i > 1, s(i) = s(i-1) + gcd(s(i-1), i). Start with the list of positive integers and remove any k's for which S(k) merges with an S(m) with m < k. Each value k > 1 is conjectural.

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A166945 Records of first differences of A166944.

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A166944 a(1)=2; a(n) = a(n-1) + gcd(n, a(n-1)) if n is even, a(n) = a(n-1) + gcd(n-2, a(n-1)) if n is odd.

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A137613 Omit the 1's from Rowland's sequence f(n) - f(n-1) = gcd(n,f(n-1)), where f(1) = 7.

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