A179382 -id:A179382 - cp's OEIS frontend

A179383 a(n) = 2*k(n)-1 where k(n) is the sequence of positions of records in A179382.

1, 5, 9, 11, 13, 19, 25, 29, 37, 53, 59, 61, 67, 83, 101, 107, 121, 131, 139, 149, 163, 173, 179, 181, 197, 211, 227, 269, 293, 317, 347, 349, 373, 379, 389, 419, 421, 443, 461, 467, 491, 509, 523, 541, 547, 557, 563, 587, 613, 619, 653, 659, 661, 677, 701, 709, 757

Offset: 1

Vladimir Shevelev, Jul 12 2010

nonn

Records in A179382(k(n)) = 1, 2, 3, 5, 6, 9, 10, 14, 18, 26, 29, ....
are located at k(n) = 1, 3, 5, 6, 7, 10, 13, 15, 19, 27, 30, 31,..
The current sequence is a simple transformation of this k(n) sequence.
Question: Are there any terms in the sequence with two or more distinct prime divisors?
Some very plausible conjectures: 1) The sequence consists of primes and squares of primes; 2) The set of squares is finite; 3) A prime p>=5 is in the sequence iff it has primitive root 2 (A001122) ; 4) There exists l such that, for n>l, A179383(n) =A139099(n+l) . [From Vladimir Shevelev , Jul 14 2010]

Peter J. C. Moses, Table of n, a(n) for n = 1..8500

Cf. A139099, A167791, A002326, A179382

Definition rephrased and sequence extended by R. J. Mathar, Jul 13 2010

I made a change to Conjecture 4). - Vladimir Shevelev, Jul 18 2010

A179686 Let m > k > 0 be odd numbers and operations "m<+>k" and "m<->k" be defined as in A179382 and A179480. Then the sequence m<+>k, m<->(m<+>k), m<+>(m<->(m<+>k)), ... is periodic; a(n) is its smallest period starting from the seeds m=2*n-1 and k=1.

Original entry on oeis.org

1, 2, 4, 2, 2, 2, 4, 2, 6, 4, 4, 6, 8, 6, 4, 2, 4, 10, 4, 6, 2, 4, 12, 12, 4, 14, 12, 2, 14, 14, 4, 2, 18, 12, 16, 4, 8, 16, 16, 14, 18, 4, 12, 4, 4, 4, 20, 10, 6, 22, 24, 4, 26, 6, 16, 6, 20, 4, 12, 26, 8, 22, 4, 2, 34, 8, 20, 14, 34, 24, 32, 6, 20, 42, 4, 12, 8, 10, 24

Offset: 2

Vladimir Shevelev, Jul 24 2010

nonn

			If n=4, 2*n-1=7, then we have 7<+>1=1, 7<->1=3, 7<+>3=5, 7<->5=1. Thus a(4)=4.

Cf. A179382, A179480.

pidx := proc(L,n,m)
    for i from 1 to nops(L)-1 do
        if [op(i..i+1,L)] = [n,m] then
            return i;
        end if;
    end do:
    return -1 ;
end proc:
A179686aux := proc(x, y) local xtrack, xitr, p;
    xtrack := [A000265(x+y)] ;
    while true do
        if type(nops(xtrack),'odd') then
            xitr := A000265(x-op(-1, xtrack)) ;
        else
            xitr := A000265(x+op(-1, xtrack)) ;
        end if;
            xtrack := [op(xtrack),xitr] ;
        p := pidx(xtrack,op(-2,xtrack),op(-1,xtrack)) ;
        if p >=1 and p < nops(xtrack) -2 then
            return nops(xtrack)-p-1 ;
        end if;
    end do:
end proc:
A179686 := proc(n)
    if n = 2 then
        1;
    else
        A179686aux(2*n-1,1) ;
    end if;
end proc:
seq(A179686(n),n=2..80) ; # R. J. Mathar, Dec 04 2011

Extended beyond a(24) by R. J. Mathar, Dec 04 2011

A179460 Numbers m for which 2*A179382(m)=A002326(m-1).

Original entry on oeis.org

2, 3, 5, 6, 7, 9, 10, 13, 14, 15, 17, 19, 21, 22, 27, 29, 30, 31, 33, 34, 35, 39, 41, 42, 49, 50, 51, 54, 55, 57, 61, 63, 65, 66, 69, 70, 71, 73, 75, 79, 82, 85, 86, 87, 89, 90, 91, 93, 97, 99, 101, 102, 103, 104, 105, 106, 107, 114, 115, 121, 122, 125, 126, 129, 133, 135

Offset: 1

Vladimir Shevelev, Jul 14 2010

nonn

m is in the sequence iff the set {1,2,...,2^(2*m-2)} considered in reduced residue system modulo 2*m-1 contains the same number of odd and even integers.

			5 in the sequence since modulo 2*5-1=9 we have {1,2,4,8,16,32}={1,2,4,8,7,5} and the last set contains 3 odd and 3 even elements.

Cf. A002326, A179382.

fQ[n_] := Block[{r = Union@ PowerMod[2, Range[0, 2 n - 2], 2 n - 1]}, Length@ r == 2 Count[ OddQ@ r, True]]; Select[ Range@ 138, fQ] (* Robert G. Wilson v, Aug 26 2010 *)

More terms from Robert G. Wilson v, Aug 26 2010

A225759 Primes p such that A179382((p+1)/2) = (p-1)/16.

Original entry on oeis.org

1217, 1249, 1553, 4049, 4273, 4481, 4993, 5297, 6449, 6481, 6689, 7121, 8081, 8609, 9137, 9281, 10337, 10369, 10433, 11617, 11633, 12577, 13441, 13633, 14321, 14753, 15569, 16417, 16433, 16673, 17137, 18257, 18433, 18481, 19793, 20113, 20353, 23057, 23857

Offset: 1

Lear Young, May 15 2013

nonn

Let n be a natural number coprime to 10 and let c be the "cycle length of n" (defined below).
Conjecture 1: If n-1=2^x*c for some x<5, then n is prime. If x > 4, the relative density of primes in such numbers is 1.
Conjecture 2: If the period of the decimal expansion of 1/n is n-1 or a divisor of n-1, and if n-1=2^x*c or n+1=2^x*c for some x, then n is prime.
- Lear Young, with contributions from Peter Košinár, Giovanni Resta, Charles R Greathouse IV, May 22 2013
To define the "cycle length of n" (using n=73 as an example):
Step 1 : 73 +  1 =  74. Get the odd part of  74, which is 37
Step 2 : 73 + 37 = 110. Get the odd part of 110, which is 55
Step 3 : 73 + 55 = 128. Get the odd part of 128, which is  1
Continuing this operation (with 73+1) repeats the same steps as above. There are 3 steps in the cycle, so the cycle length of 73 is c=3. (same to A179382((73+1)/2)=3).
More for the "cycle length of n" see link and cross references.
The numbers in the sequence are the values of n in the above conjecture when c=4 in case (1).

			(1217-1)/16 = 76 = A179382(609).

Lear Young and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 117 terms from Young)
Hagen von Eitzen, Details of the "cycle length of n"

Analogs with different values of c: A001122 when c=1, A155072 when c=2, A001134 when c=3. A225890 has composite values.

Cf. A179382, A136042 (both sequences related to the way to get the "cycle length of n").

oddres(n)=n>>valuation(n, 2)
cyc(d)=my(k=1, t=1); while((t=oddres(t+d))>1, k++); k
forstep(n=17,1e4,[32,16],if(cyc(n)==n>>4 && isprime(n), print1(n", ")))
\\ Charles R Greathouse IV, May 15 2013

Edited by Charles R Greathouse IV, Nov 11 2014

A225890 Composite numbers n such that A179382((n+1)/2)=(n-1)/(2^c) for some c > 0.

Original entry on oeis.org

92673, 143713, 3579553, 4110529, 28688897, 127017857, 141127681, 157648097, 162101441

Offset: 1

Lear Young and Peter Košinár, May 20 2013

a(10) > 180*10^6. All terms up to a(9) are of the form 32*k+1 and except a(1) are also semiprimes. The numbers 212999489, 393300097 and 663414881 are also terms. - Giovanni Resta, May 21 2013

			143713=137*1049: A179382((143713+1)/2)=4491=(143713-1)/(2^5)

Cf. A179382.

oddres(n)=n>>valuation(n, 2)
cyc(d)=my(k=1, t=1); while((t=oddres(t+d))>1, k++); k
p=5;forprime(q=7,1e7,forstep(n=p+2, q-2, 2, my(t=(n-1)/cyc(n), c=valuation(t,2)); if(t>>c==1 && c>0, print1(n", ")));p=q) \\ Charles R Greathouse IV, May 20 2013

Missing a(3) from Giovanni Resta, May 20 2013

a(6)-a(9) from Giovanni Resta, May 21 2013

A179541 a(n) is the least possible smallest period attainable by the action of a periodic sequence of binary operations <+>,<-> (see A179382,A179480), beginning with 2n-1<+>1 or 2n-1<->1.

Original entry on oeis.org

1, 1, 1, 1, 2, 2, 1, 1, 3, 2, 4

Offset: 2

Vladimir Shevelev, Jul 18 2010

nonn

The minorizing sequence for all sequences of type A179382,A179480 with arbitrary periodic rotation of the binary operations <+>,<->.

			Let n=12, 2n-1=23. Considering periodic sequence <+>,<->,<+>,<->,..., we have 23<+>1=3, 23<->3=5, 23<+>5=7, 23<->7=1, 23<+>1=3,... Thus a(12)<=4. It is not difficult to verify that a(12)>3. Thus a(12)=4.

Cf. A179382 A179480

A225913 Composite numbers coprime to 6 such that A179382(n) = A000265(n-1), the odd part of n-1.

Original entry on oeis.org

517, 1525, 1765, 1837, 2941, 3241, 3265, 3397, 3421, 3565, 4117, 4501, 4669, 6349, 7357, 8569, 8749, 8965, 9085, 9997, 10045, 10057, 10981, 11929, 13741, 14101, 15757, 16117, 18745, 18949, 18997, 19885, 20557, 20629, 21805, 22045, 22645, 24445, 24505, 25417, 25429, 25681, 25885, 25957, 26101, 26245, 27205

Offset: 1

M. F. Hasler, May 20 2013

nonn

Inspired by the Conjecture mentioned in A225759.

forstep(n=1,9e9,6, A179382(n)==(n-1)>>valuation(n-1,2) & !isprime(n) & print1(n","))

A226014 Primes p such that A179382((p+1)/2) = (p-1)/(2^x) for some x>0.

Original entry on oeis.org

3, 7, 11, 13, 17, 19, 29, 31, 37, 41, 53, 59, 61, 67, 83, 97, 101, 107, 113, 127, 131, 137, 139, 149, 163, 173, 179, 181, 193, 197, 211, 227, 257, 269, 281, 293, 313, 317, 347, 349, 353, 373, 379, 389, 401, 409, 419, 421, 443, 449, 461, 467, 491, 509, 521, 523, 541, 547, 557, 563, 569, 577, 587, 593, 613, 617, 619, 653, 659, 661, 677, 701, 709, 757, 761, 769, 773, 787, 797, 809, 821, 827, 829, 853, 857, 859, 877, 883, 907, 929, 941, 947, 977

Offset: 1

Lear Young, May 22 2013

It is conjectured that:
Let n be an odd number and the period of 1/n is n-1 or a divisor of n-1. Call c=A179382((n+1)/2) the "cycle length of n". If c divides n-1 or n+1 = 2^x for some x>0, then n is prime. For details see link and Cf. - Lear Young, with contributions from Peter Košinár, Giovanni Resta, Charles R Greathouse IV, May 22 2013
The numbers in the sequence are the values of n in the above conjecture.

			929 : (929-1)/(2^2)=232=A179382((929+1)/2) and znorder(Mod(10,929))=464=(929-1)/2

Hagen von Eitzen, Details of the "cycle length of n"

Cf. A179382, A136042 (both sequences related to the way to get the "cycle length of n").

oddres(n)=n>>valuation(n, 2)
cyc(d)=my(k=1, t=1); while((t=oddres(t+d))>1, k++); k
forstep(n=3, 1e3, [4, 2, 2, 2], x=cyc(n);z=znorder(Mod(10, n));if((x==1 || (n%x==1 && oddres((n-1)/x)==1)) && (n%z==1 || n%z==0), print1(n", ")))
\\ Charles R Greathouse IV, May 22 2013

A001122 Primes with primitive root 2.

Original entry on oeis.org

3, 5, 11, 13, 19, 29, 37, 53, 59, 61, 67, 83, 101, 107, 131, 139, 149, 163, 173, 179, 181, 197, 211, 227, 269, 293, 317, 347, 349, 373, 379, 389, 419, 421, 443, 461, 467, 491, 509, 523, 541, 547, 557, 563, 587, 613, 619, 653, 659, 661, 677, 701, 709, 757, 773, 787, 797

Offset: 1

N. J. A. Sloane

Artin conjectured that this sequence is infinite.
Conjecture: sequence contains infinitely many pairs of twin primes. - Benoit Cloitre, May 08 2003
Pieter Moree writes (Oct 20 2004): Assuming the Generalized Riemann Hypothesis, it can be shown that the density of primes p such that a prescribed integer g has order (p-1)/t, with t fixed, exists and, moreover, it can be computed. This density will be a rational number times the so-called Artin constant. For 2 and 10 the density of primitive roots is A, the Artin constant itself.
It seems that this sequence consists of A050229 \ {1,2}.
Primes p such that 1/p, when written in base 2, has period p-1, which is the greatest period possible for any integer.
Positive integer 2*m-1 is in the sequence iff A179382(m)=m-1. - Vladimir Shevelev, Jul 14 2010
These are the odd primes p for which the polynomial 1+x+x^2+...+x^(p-1) is irreducible over GF(2). - V. Raman, Sep 17 2012 [Corrected by N. J. A. Sloane, Oct 17 2012]
Prime(n) is in the sequence if (and conjecturally only if) A133954(n) = prime(n). - Vladimir Shevelev, Aug 30 2013
Pollack shows that, on the GRH, that there is some C such that a(n+1) - a(n) < C infinitely often (in fact, 1 can be replaced by any positive integer). Further, for any m, a(n), a(n+1), ..., a(n+m) are consecutive primes infinitely often. - Charles R Greathouse IV, Jan 05 2015
From Jianing Song, Apr 27 2019: (Start)
All terms are congruent to 3 or 5 modulo 8. If we define
  Pi(N,b) = # {p prime, p <= N, p == b (mod 8)};
     Q(N) = # {p prime, p <= N, p in this sequence},
then by Artin's conjecture, Q(N) ~ C*N/log(N) ~ 2*C*(Pi(N,3) + Pi(N,5)), where C = A005596 is Artin's constant.
Conjecture: if we further define
   Q(N,b) = # {p prime, p <= N, p == b (mod 8), p in this sequence},
then we have:
   Q(N,3) ~ (1/2)*Q(N) ~ C*Pi(N,3);
   Q(N,5) ~ (1/2)*Q(N) ~ C*Pi(N,5). (End)
Conjecture: for a prime p > 5, p has primitive root 2 iff p == +-3 (mod 8) divides 2^k + 3 for some k < p - 1 and divides 2^m + 5 for some m < p - 1. It seems that all primes of the form 2^k + 3 for k <> 2 (A057732) have primitive root 2. - Thomas Ordowski, Nov 27 2023

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 864.
E. Bach and Jeffrey Shallit, Algorithmic Number Theory, I; see p. 221.
J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, New York, 1996; see p. 169.
M. Kraitchik, Recherches sur la Théorie des Nombres. Gauthiers-Villars, Paris, Vol. 1, 1924, Vol. 2, 1929, see Vol. 1, p. 56.
Lehmer, D. H. and Lehmer, Emma; Heuristics, anyone? in Studies in mathematical analysis and related topics, pp. 202-210, Stanford Univ. Press, Stanford, Calif., 1962.
Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 20.
D. Shanks, Solved and Unsolved Problems in Number Theory, 2nd. ed., Chelsea, 1978, p. 81.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Antti Karttunen, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
Joerg Arndt, Matters Computational (The Fxtbook), pp. 876-878.
Richard Bartels, Generalized Loewy Length of Cohen-Macaulay Local and Graded Rings, arXiv:2308.14932 [math.AC], 2023. See p. 10.
J. Conde, M. Miller, J. M. Miret, and K. Saurav, On the Nonexistence of Almost Moore Digraphs of Degree Four and Five, Mathematics in Computer Science, 9(2) (2015), 145-149.
Jonathan Detchart and Jérôme Lacan, Improving the coding speed of erasure codes with polynomial ring transforms, arXiv:1709.00178 [cs.IT], 2017.
K. Dilcher and L. Ericksen, Reducibility and irreducibility of Stern (0, 1)-polynomials, Communications in Mathematics, 22 (2014), 77-102.
Gabriele Fici and Estéban Gabory, Generalized De Bruijn Words, Invertible Necklaces, and the Burrows-Wheeler Transform, arXiv:2502.12844 [math.CO], 2025. See p. 12.
R. Gupta and M. R. Murty, A remark on Artin's conjecture, Invent. Math. 78 (1984), 127-230.
C. Hooley, On Artin's conjecture, J. Reine Angewandte Math., 225 (1967), 209-220.
Florian Ingels, Anaïs Denis, and Bastien Cazaux, Decomposing Words for Enhanced Compression: Exploring the Number of Runs in the Extended Burrows-Wheeler Transform, arXiv:2506.04926 [cs.DS], 2025. See p. 15.
Robert Jackson, Dmitriy Rumynin and Oleg V. Zaboronski, An approach to RAID-6 based on cyclic groups, Applied Mathematics & Information Sciences, 5(2) (2011), 148-170.
Jonas Kaiser, On the relationship between the Collatz conjecture and Mersenne prime numbers, arXiv:1608.00862 [math.GM], 2016.
Sihem Mesnager and Jean-Pierre Flori, A note on hyper-bent functions via Dillon-like exponents, IACR, Report 2012/033, 2012.
F. Pillichshammer, Bounds for the quality parameter of digital shift nets over Z_2, Finite Fields Applic., 8 (2002), 444-454.
Pieter Moree, Artin's primitive root conjecture-a survey, arXiv:math/0412262 [math.NT], 2004-2012.
Paul Pollack, Bounded gaps between primes with a given primitive root, arXiv:1404.4007 [math.NT], 2014.
Vladimir Shevelev, On the Newman sum over multiples of a prime with a primitive or semiprimitive root 2, arXiv:0710.1354 [math.NT], 2007.
Stephan Tornier, Groups Acting on Trees With Prescribed Local Action, arXiv:2002.09876 [math.GR], 2020.
Qifu Tyler Sun, Hanqi Tang, Zongpeng Li, Xiaolong Yang, and Keping Long, Circular-shift Linear Network Codes with Arbitrary Odd Block Lengths, arXiv:1806.04635 [cs.IT], 2018.
Eric Weisstein's World of Mathematics, Artin's constant.
Wikipedia, Artin's conjecture on primitive roots.
Index entries for sequences related to Artin's conjecture
Index entries for primes by primitive root

Cf. A001123, A001913, A001917, A005596 (Artin's constant), A050229, A071642, A127209, A163782, A292270.
Cf. A002326 for the multiplicative order of 2 mod 2n+1. (Alternatively, the least positive value of m such that 2n+1 divides 2^m-1).
Cf. A216838 (Odd primes for which 2 is not a primitive root).

Select[ Prime@Range@200, PrimitiveRoot@# == 2 &] (* Robert G. Wilson v, May 11 2001 *)
pr = 2; Select[Prime[Range[200]], MultiplicativeOrder[pr, # ] == # - 1 &] (* N. J. A. Sloane, Jun 01 2010 *)

forprime(p=3, 1000, if(znorder(Mod(2, p))==(p-1), print1(p,", "))); \\ [corrected by Michel Marcus, Oct 08 2014]

from itertools import islice
from sympy import nextprime, is_primitive_root
def A001122_gen(): # generator of terms
    p = 2
    while (p:=nextprime(p)):
        if is_primitive_root(2,p):
            yield p
A001122_list = list(islice(A001122_gen(),30)) # Chai Wah Wu, Feb 13 2023

Delta(a(n),2^a(n)*x) = a(n)*Delta(a(n),2*x), where Delta(k,x) is the difference between numbers of evil(A001969) and odious(A000069) integers divisible by k in interval [0,x). - Vladimir Shevelev, Aug 30 2013

For n >= 2, a(n) = 1 + 2*A163782(n-1). - Antti Karttunen, Oct 07 2017

A179480 Let m>k>0 be odd numbers and denote by the symbol "m<->k" the value A000265(m-k). Then the sequence m<->k, m<->(m<->k), m<->(m<->(m<->k)), ... is periodic; a(n) is the smallest period in the case m=2*n-1, k=1.

Original entry on oeis.org

1, 1, 2, 1, 3, 3, 2, 1, 5, 2, 6, 5, 5, 7, 2, 1, 6, 9, 6, 3, 3, 6, 12, 10, 4, 13, 10, 3, 15, 15, 2, 1, 17, 10, 18, 2, 10, 14, 20, 13, 21, 2, 14, 4, 6, 4, 18, 11, 9, 25, 26, 4, 27, 9, 18, 5, 22, 4, 12, 27, 10, 25, 2, 1, 33, 6, 18, 15, 35, 22, 30, 3, 22, 37, 6, 12, 10, 13, 26

Offset: 2

Vladimir Shevelev, Jul 16 2010

nonn

A dual sequence to A179382.
Let b = (2*n-1) and k = A003558(n-1). If a(n) is odd, b divides (2^k + 1); but if a(n) is even, b divides (2^k - 1). Examples: a(14) = 5, odd; with b = 27 and A003558(13) = 9. Then 27 divides (2^9 + 1) or 513 = 27 * 19. a(18) = 6, even. b = 35, with k= A003558(17) = 12. Then 35 divides (2^12 - 1). - Gary W. Adamson, Aug 20 2012.
Iff a(n) = n/2 or (n-1)/2, then 2*n - 1 is a prime with one coach and is in A216371. Examples: a(19) = 9, so 37 is in A216371. a(12) = 6, so 23 is in A216371. - _Gary W. Adamson, Sep 08 2012.

			If n=14, then m=27 and we have 27<->1=13, 27<->13=7, 27<->7=5, 27<->5=11, 27<->11=1. Thus a(14)=5.

Cf. A179382, A179383, A000265.
Cf. A003558.
Cf. A216371.

Contribution from R. J. Mathar, Nov 04 2010: (Start)
A179480aux := proc(x,y) local xtrack,xitr,xpos ; xtrack := [y] ; while true do xitr := A000265(x-op(-1,xtrack)) ; if not member(xitr, xtrack,'xpos') then xtrack := [op(xtrack),xitr] ; else return 1+nops(xtrack)-xpos ; end if; end do: end proc:
A179480 := proc(n) A179480aux(2*n-1,1) ; end proc: seq(A179480(n),n=2..80) ; (End)

oddres[n_] := n/2^IntegerExponent[n, 2];
b[x_, y_] := Module[{xtrack = {y}, xitr}, While[True, xitr = oddres[x - Last@ xtrack]; If[FreeQ[xtrack, xitr], AppendTo[xtrack, xitr], Return[ Length[xtrack]]]]];
a[n_] := b[2n-1, 1];
a /@ Range[2, 80] (* Jean-François Alcover, Apr 13 2020, after R. J. Mathar *)

Edited by N. J. A. Sloane, Jul 18 2010

More terms from R. J. Mathar, Nov 04 2010

cp's OEIS Frontend

A179383 a(n) = 2*k(n)-1 where k(n) is the sequence of positions of records in A179382.

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A179686 Let m > k > 0 be odd numbers and operations "m<+>k" and "m<->k" be defined as in A179382 and A179480. Then the sequence m<+>k, m<->(m<+>k), m<+>(m<->(m<+>k)), ... is periodic; a(n) is its smallest period starting from the seeds m=2*n-1 and k=1.

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A179460 Numbers m for which 2*A179382(m)=A002326(m-1).

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A225759 Primes p such that A179382((p+1)/2) = (p-1)/16.

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A225890 Composite numbers n such that A179382((n+1)/2)=(n-1)/(2^c) for some c > 0.

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A179541 a(n) is the least possible smallest period attainable by the action of a periodic sequence of binary operations <+>,<-> (see A179382,A179480), beginning with 2n-1<+>1 or 2n-1<->1.

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A225913 Composite numbers coprime to 6 such that A179382(n) = A000265(n-1), the odd part of n-1.

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A226014 Primes p such that A179382((p+1)/2) = (p-1)/(2^x) for some x>0.

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A001122 Primes with primitive root 2.

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