A001567 -id:A001567 - cp's OEIS frontend

A065341 Mersenne composites: 2^prime(m) - 1 is not a prime.

2047, 8388607, 536870911, 137438953471, 2199023255551, 8796093022207, 140737488355327, 9007199254740991, 576460752303423487, 147573952589676412927, 2361183241434822606847, 9444732965739290427391

Offset: 1

Labos Elemer, Oct 30 2001

nonn

For the number of prime factors in a(n) see A135975. For indices of primes n in composite 2^prime(n)-1 see A135980. For smallest prime divisors of Mersenne composites see A136030. For largest prime divisors of Mersenne composites see A136031. For largest divisors see A145097. - Artur Jasinski, Oct 01 2008

All the terms are Fermat pseudoprimes to base 2 (A001567). For a proof see, e.g., Jaroma and Reddy (2007). - Amiram Eldar, Jul 24 2021

			2^11 - 1 = 2047 = 23*89.

Muniru A Asiru, Table of n, a(n) for n = 1..110
John H. Jaroma and Kamaliya N. Reddy, Classical and alternative approaches to the Mersenne and Fermat numbers, The American Mathematical Monthly, Vol. 114, No. 8 (2007), pp. 677-687.

Cf. A054723, A000043, A000668, A001348, A001567.

Cf. A135975, A135980, A145097, A136031. - Artur Jasinski, Oct 01 2008

A065341 := proc(n) local i;
i := 2^(ithprime(n))-1:
if (not isprime(i)) then
   RETURN (i)
fi: end: seq(A065341(n), n=1..21); # Jani Melik, Feb 09 2011

Select[Table[2^Prime[n]-1,{n,30}],!PrimeQ[#]&] (* Harvey P. Dale, May 06 2018 *)

a(n) = 2^A054723(n) - 1.

A005936 Pseudoprimes to base 5.

Original entry on oeis.org

4, 124, 217, 561, 781, 1541, 1729, 1891, 2821, 4123, 5461, 5611, 5662, 5731, 6601, 7449, 7813, 8029, 8911, 9881, 11041, 11476, 12801, 13021, 13333, 13981, 14981, 15751, 15841, 16297, 17767, 21361, 22791, 23653, 24211, 25327, 25351, 29341, 29539

Offset: 1

N. J. A. Sloane

nonn

According to Karsten Meyer, 4 should be excluded, following the strict definition in Crandall and Pomerance. - May 16 2006
Theorem: If both numbers q and (2q - 1) are primes (q is in the sequence A005382) then n = q*(2q - 1) is a pseudoprime to base 5 (n is in the sequence) if and only if q is of the form 10k + 1. 1891, 88831, 146611, 218791, 721801, ... are such terms. This sequence is a subsequence of A122782. - Farideh Firoozbakht, Sep 14 2006
Composite numbers n such that 5^(n-1) == 1 (mod n).

R. Crandall and C. Pomerance, "Prime Numbers - A Computational Perspective", Second Edition, Springer Verlag 2005, ISBN 0-387-25282-7 Page 132 (Theorem 3.4.2. and Algorithm 3.4.3)
J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 124, p. 43, Ellipses, Paris 2008.
R. K. Guy, Unsolved Problems in Number Theory, A12.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

R. J. Mathar, T. D. Noe and Hiroaki Yamanouchi, Table of n, a(n) for n = 1..92893 (terms a(1)-a(776) from R. J. Mathar, a(777)-a(1000) from T. D. Noe)
J. Bernheiden, Pseudoprimes (Text in German)
C. Pomerance & N. J. A. Sloane, Correspondence, 1991
F. Richman, Primality testing with Fermat's little theorem
Eric Weisstein's World of Mathematics, Fermat Pseudoprime
Index entries for sequences related to pseudoprimes

Pseudoprimes to other bases: A001567 (2), A005935 (3), A005937 (6), A005938 (7), A005939 (10).

Cf. A005382, A122782.

base = 5; t = {}; n = 1; While[Length[t] < 100, n++; If[! PrimeQ[n] && PowerMod[base, n-1, n] == 1, AppendTo[t, n]]]; t (* T. D. Noe, Feb 21 2012 *)
Select[Range[30000],CompositeQ[#]&&PowerMod[5,#-1,#]==1&] (* Harvey P. Dale, Jul 21 2023 *)

More terms from David W. Wilson, Aug 15 1996

A007013 Catalan-Mersenne numbers: a(0) = 2; for n >= 0, a(n+1) = 2^a(n) - 1.

Original entry on oeis.org

2, 3, 7, 127, 170141183460469231731687303715884105727

Offset: 0

N. J. A. Sloane, Nik Lygeros (webmaster(AT)lygeros.org)

nonn

The next term is too large to include.
Orbit of 2 under iteration of the "Mersenne operator" M: n -> 2^n-1 (0 and 1 are fixed points of M). - M. F. Hasler, Nov 15 2006
Also called the Catalan sequence. - Artur Jasinski, Nov 25 2007
a(n) divides a(n+1)-1 for every n. - Thomas Ordowski, Apr 03 2016
Proof: if 2^a == 2 (mod a), then 2^a = 2 + ka for some k, and 2^(2^a-1) = 2^(1 + ka) = 2*(2^a)^k == 2 (mod 2^a-1). Given that a(1) = 3 satisfies 2^a == 2 (mod a), that gives you all 2^a(n) == 2 (mod a(n)), and since a(n+1) - 1 = 2^a(n) - 2 that says a(n) | a(n+1) - 1. - Robert Israel, Apr 05 2016
All terms shown are primes, the status of the next term is currently unknown. - Joerg Arndt, Apr 03 2016
The next term is a prime or a Fermat pseudoprime to base 2 (i.e., a member of A001567). If it is a pseudoprime, then all succeeding terms are pseudoprimes. - Thomas Ordowski, Apr 04 2016
a(n) is the least positive integer that requires n+1 steps to reach 1 under iteration of the binary weight function A000120. - David Radcliffe, Jun 25 2018
If the next term were prime, it would be a counterexample to the New Mersenne conjecture. It is known that (2^a(4) + 1) / 3 is composite, with factor 886407410000361345663448535540258622490179142922169401 = 5209834514912200*a(4)+1. - William Hu, Jul 30 2024
a(n) is the smallest number of additive persistence n+1 in base 2.  (Similar to A006050 but for binary instead of decimal.) - J. Beach, Nov 17 2024

P. Ribenboim, The Book of Prime Number Records. Springer-Verlag, NY, 2nd ed., 1989, p. 81.
W. Sierpiński, A Selection of Problems in the Theory of Numbers. Macmillan, NY, 1964, p. 91.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Chris K. Caldwell, Mersenne Primes.
Alex Kritov, Explicit Values for Gravitational and Hubble Constants from Cosmological Entropy Bound and Alpha-Quantization of Particle Masses, 2021, see p. 8.
Double Mersennes Prime Search Status of M(M(p)) where M(p) is a Mersenne prime [outdated link of Will Edgington replaced by _Georg Fischer_, Jan 18 2019].
Carlos Rivera, Conjecture 15. The New Mersenne Conjecture, The Prime Puzzles & Problems Connection.
W. Sierpiński, A Selection of Problems in the Theory of Numbers, Macmillan, NY, 1964, p. 91-92. (Annotated scanned copy)
Eric Weisstein's World of Mathematics, Catalan-Mersenne Number
Eric Weisstein's World of Mathematics, Double Mersenne Number.

Cf. A000668, A001567, A014221, A006050, A180094.

M:=n->2^n-1; '(M@@i)(2)'$i=0..4; # M. F. Hasler, Nov 15 2006

NestList[2^#-1&,2,4] (* Harvey P. Dale, Jul 18 2011 *)

a(n)=if(n,2^a(n-1)-1,2) \\ Charles R Greathouse IV, Sep 07 2016

a(n) = M(a(n-1)) = M^n(2) with M: n-> 2^n-1. - M. F. Hasler, Nov 15 2006

A180094(a(n)) = n + 1.

Edited by Henry Bottomley, Nov 07 2002

Amended title name by Marc Morgenegg, Apr 14 2016

A050217 Super-Poulet numbers: Poulet numbers whose divisors d all satisfy d|2^d-2.

Original entry on oeis.org

341, 1387, 2047, 2701, 3277, 4033, 4369, 4681, 5461, 7957, 8321, 10261, 13747, 14491, 15709, 18721, 19951, 23377, 31417, 31609, 31621, 35333, 42799, 49141, 49981, 60701, 60787, 65077, 65281, 80581, 83333, 85489, 88357, 90751

Offset: 1

Eric W. Weisstein

nonn

Every semiprime in A001567 is in this sequence (see Sierpiński). a(61) = 294409 is the first term having more than two prime factors. See A178997 for super-Poulet numbers having more than two prime factors. - T. D. Noe, Jan 11 2011
Composite numbers n such that 2^d == 2 (mod n) for every d|n. - Thomas Ordowski, Sep 04 2016
Composite numbers n such that 2^p == 2 (mod n) for every prime p|n. - Thomas Ordowski, Sep 06 2016
Composite numbers n = p(1)^e(1)*p(2)^e(2)*...*p(k)^e(k) such that 2^gcd(p(1)-1,p(2)-1,...,p(k)-1) == 1 (mod n). - Thomas Ordowski, Sep 12 2016
Nonsquarefree terms are divisible by the square of a Wieferich prime (see A001220). These include 1194649, 12327121, 5654273717, 26092328809, 129816911251. - Robert Israel, Sep 13 2016
Composite numbers n such that 2^A258409(n) == 1 (mod n). - Thomas Ordowski, Sep 15 2016

W. Sierpiński, Elementary Theory of Numbers, Warszawa, 1964, p. 231.

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)
Eric Weisstein's World of Mathematics, Super-Poulet Numbers
Wikipedia, Super-Poulet number

A214305 is a subsequence.
A065341 is a subsequence. - Thomas Ordowski, Nov 20 2016
Cf. A001220, A001567, A178997.

filter:= = proc(n)
    not isprime(n) and andmap(p -> 2&^p mod n = 2, numtheory:-factorset(n))
end proc:
select(filter, [seq(i,i=3..10^5,2)]); # Robert Israel, Sep 13 2016

Select[Range[1, 110000, 2], !PrimeQ[#] && Union[PowerMod[2, Rest[Divisors[#]], #]] == {2} & ]

is(n)=if(isprime(n), return(0)); fordiv(n,d, if(Mod(2,d)^d!=2, return(0))); n>1 \\ Charles R Greathouse IV, Aug 27 2016

A005938 Pseudoprimes to base 7.

Original entry on oeis.org

6, 25, 325, 561, 703, 817, 1105, 1825, 2101, 2353, 2465, 3277, 4525, 4825, 6697, 8321, 10225, 10585, 10621, 11041, 11521, 12025, 13665, 14089, 16725, 16806, 18721, 19345, 20197, 20417, 20425, 22945, 25829, 26419, 29234, 29341, 29857, 29891, 30025, 30811, 33227

Offset: 1

N. J. A. Sloane

nonn

According to Karsten Meyer, May 16 2006, 6 should be excluded, following the strict definition in Crandall and Pomerance.
Theorem: If both numbers q & 2q-1 are primes(q is in the sequence A005382) and n=q*(2q-1) then 7^(n-1)==1 (mod 7)(n is in the sequence) iff q=2 or mod(q,14) is in the set {1, 5, 13}. 6,703,18721,38503,88831,104653,146611,188191,... are such terms. This sequence is a subsequence of A122784. - Farideh Firoozbakht, Sep 14 2006
Composite numbers n such that 7^(n-1) == 1 (mod n).

R. Crandall and C. Pomerance, "Prime Numbers - A Computational Perspective", Second Edition, Springer Verlag 2005, ISBN 0-387-25282-7 Page 132 (Theorem 3.4.2. and Algorithm 3.4.3)
R. K. Guy, Unsolved Problems in Number Theory, A12.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

R. J. Mathar, T. D. Noe and Hiroaki Yamanouchi, Table of n, a(n) for n = 1..87448 (terms a(1)-a(697) from R. J. Mathar, a(698)-a(1000) from T. D. Noe)
J. Bernheiden, Pseudoprimes (Text in German)
C. Pomerance & N. J. A. Sloane, Correspondence, 1991
F. Richman, Primality testing with Fermat's little theorem
Index entries for sequences related to pseudoprimes

Pseudoprimes to other bases: A001567 (2), A005935 (3), A005936 (5), A005937 (6), A005939 (10).

Cf. A005382, A122784.

Select[Range[31000], ! PrimeQ[ # ] && PowerMod[7, (# - 1), # ] == 1 &] (* Farideh Firoozbakht, Sep 14 2006 *)

from sympy import isprime
def ok(n): return pow(7, n-1, n) == 1 and not isprime(n)
print(list(filter(ok, range(1, 34000)))) # Michael S. Branicky, Jun 25 2021

A090086 Smallest pseudoprime to base n, not necessarily exceeding n (cf. A007535).

Original entry on oeis.org

4, 341, 91, 15, 4, 35, 6, 9, 4, 9, 10, 65, 4, 15, 14, 15, 4, 25, 6, 21, 4, 21, 22, 25, 4, 9, 26, 9, 4, 49, 6, 25, 4, 15, 9, 35, 4, 39, 38, 39, 4, 205, 6, 9, 4, 9, 46, 49, 4, 21, 10, 51, 4, 55, 6, 15, 4, 57, 15, 341, 4, 9, 62, 9, 4, 65, 6, 25, 4, 69, 9, 85, 4, 15, 74, 15, 4, 77, 6, 9, 4, 9, 21, 85, 4, 15, 86, 87, 4, 91, 6

Offset: 1

Labos Elemer, Nov 25 2003

nonn

If n-1 is composite, then a(n) < n. - Thomas Ordowski, Aug 08 2018
Conjecture: a(n) = A007535(n) for finitely many n. For n > 2; if a(n) > n, then n-1 is prime (find all these primes). - Thomas Ordowski, Aug 09 2018
It seems that if a(2^p) = p^2, then 2^p-1 is prime. - Thomas Ordowski, Aug 10 2018
a(n) is the smallest composite k such that n^(k-1) == (1-k)^n (mod k). - Thomas Ordowski, Mar 19 2025

			From _Robert G. Wilson v_, Feb 26 2015: (Start)
a(n) = 4 for n = 1 + 4*k, k >= 0.
a(n) = 6 for n = 7 + 12*k, k >= 0.
a(n) = 9 for n = 8 + 18*k, 10 + 18*k, 35 + 36*k, k >= 0.
(End)
a(n) = 10 for n = 51 + 60*k, 11 + 180*k, 131 + 180*k, k >= 0.

Robert G. Wilson v, Table of n, a(n) for n = 1..10000 (first 1024 terms from Eric Chen)
Wikipedia, Pseudoprime
Index entries for sequences related to pseudoprimes

Cf. A007535, A250200, A090085, A090087, A000790, A239293, A293203.

Cf. A001567, A005935, A005936, A005937, A005938, A005939, A020136 - A020228.

f[n_] := Block[{k = 1}, While[ GCD[n, k] > 1 || PrimeQ[k] || PowerMod[n, k - 1, k] != 1, j = k++]; k]; Array[f, 91] (* Robert G. Wilson v, Feb 26 2015 *)

/* a(n) <= 2000 is sufficient up to n = 10000 */
a(n) = for(k=2,2000,if((n^(k-1))%k==1 && !isprime(k), return(k))) \\ Eric Chen, Feb 22 2015

a(n) = {forcomposite(k=2, , if (Mod(n,k)^(k-1) == 1, return (k)););} \\ Michel Marcus, Mar 02 2015

a(n) = LeastComposite{x; n^(x-1) mod x = 1}.

A122780 Nonprimes k such that 3^k == 3 (mod k).

Original entry on oeis.org

1, 6, 66, 91, 121, 286, 561, 671, 703, 726, 949, 1105, 1541, 1729, 1891, 2465, 2665, 2701, 2821, 3281, 3367, 3751, 4961, 5551, 6601, 7107, 7381, 8205, 8401, 8646, 8911, 10585, 11011, 12403, 14383, 15203, 15457, 15841, 16471, 16531, 18721, 19345

Offset: 1

Farideh Firoozbakht, Sep 11 2006

Theorem: If q!=3 and both numbers q and (2q-1) are primes then k=q*(2q-1) is in the sequence. 6, 91, 703, 1891, 2701, 12403, 18721, 38503, 49141, ... is the related subsequence.

The terms > 1 and coprime to 3 of this sequence are the base-3 pseudoprimes, A005935. - M. F. Hasler, Jul 19 2012 [Corrected by Jianing Song, Feb 06 2019]

			66 is composite and 3^66 = 66*468229611858069884271524875811 + 3 so 66 is in the sequence.

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

Cf. A001567, A005935, A122014.

Cf. A122781, A122782, A122783, A122784, A122785, A122786.

isA122780 := proc(n)
    if isprime(n) then
        false;
    else
        modp( 3 &^ n,n) = modp(3,n) ;
    end if;
end proc:
for n from 1 do
    if isA122780(n) then
        print(n) ;
    end if;
end do: # R. J. Mathar, Jul 15 2012

Select[Range[30000], ! PrimeQ[ # ] && Mod[3^#, # ] == Mod[3, # ] &]
Join[{1},Select[Range[20000],!PrimeQ[#]&&PowerMod[3,#,#]==3&]] (* Harvey P. Dale, Apr 30 2023 *)

is_A122780(n)={n>0 & Mod(3, n)^n==3 & !ispseudoprime(n)} \\ M. F. Hasler, Jul 19 2012

A262051 Euler pseudoprimes to base 3: composite integers such that abs(3^((n - 1)/2)) == 1 mod n.

Original entry on oeis.org

121, 703, 1541, 1729, 1891, 2465, 2821, 3281, 4961, 7381, 8401, 8911, 10585, 12403, 15457, 15841, 16531, 18721, 19345, 23521, 24661, 28009, 29341, 30857, 31621, 31697, 41041, 44287, 46657, 47197, 49141, 50881, 52633, 55969, 63139, 63973, 72041, 74593, 75361

Offset: 1

Daniel Lignon, Sep 09 2015

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..64 from Daniel Lignon)

Cf. A006970 (base 2), this sequence (base 3), A001567 (base 4), A262052 (base 5), A262053 (base 6), A262054 (base 7), A262055 (base 8).

eulerPseudoQ[n_?PrimeQ, b_] = False; eulerPseudoQ[n_, b_] := Block[{p = PowerMod[b, (n - 1)/2, n]}, p == Mod[1, n] || p == Mod[-1, n]]; Select[2 Range[26000] + 1, eulerPseudoQ[#, 3] &] (* Michael De Vlieger, Sep 09 2015, after Jean-François Alcover at A006970 *)

for(n=1, 1e5, if( Mod(3, (2*n+1))^n == 1 ||  Mod(3, (2*n+1))^n == 2*n && bigomega(2*n+1) != 1 , print1(2*n+1", "))); \\ Altug Alkan, Oct 11 2015

A164333 Primes prime(k) such that all integers in the interval [(prime(k-1)+1)/2, (prime(k)-1)/2] are composite numbers.

Original entry on oeis.org

13, 19, 31, 43, 53, 61, 71, 73, 101, 103, 109, 113, 131, 139, 151, 157, 173, 181, 191, 193, 199, 229, 233, 239, 241, 251, 269, 271, 283, 293, 311, 313, 349, 353, 373, 379, 409, 419, 421, 433, 439, 443, 463, 491, 499, 509, 523, 571, 577, 593, 599, 601, 607, 613, 619, 643

Offset: 1

Vladimir Shevelev, Aug 13 2009

nonn

Let p_k be the k-th prime. A prime p is in the sequence iff the interval of the form (2p_k, 2p_(k+1)), containing p, also contains a prime less than p. The sequence is connected with the following classification of primes: the first two primes 2,3 form a separate set of primes; let p >= 5 be in the interval (2p_k, 2p_(k+1)), then 1) if in this interval there are only primes greater than p, then p is called a right prime; 2) if in this interval there are only primes less than p, then p is called a left prime; 3) if in this interval there are primes both greater and less than p, then p is called a central prime; 4) if this interval does not contain other primes, then p is called an isolated prime. In particular, the right primes form sequence A166307, and all Ramanujan primes (A104272) greater than 2 are either right or central primes; the left primes form sequence A182365, and all Labos primes (A080359) greater than 3 are either left or central primes; the central primes form A166252 and the isolated primes form A166251. [Vladimir Shevelev, Oct 10 2009] [Sequence reference updated by Peter Munn, Jun 01 2023]

Disjoint union of A166252 and A182365. - Peter Munn, Jun 01 2023 [an edited version of a contribution by Vladimir Shevelev in 2009]

			Let p=53. We see that 2*23<53<2*29. Since the interval (46, 58) contains prime 47<53 and does not contain any prime more than 53, then, by the considered classification 53 is left prime and it is in the sequence. [_Vladimir Shevelev_, Oct 10 2009]

V. Shevelev, On critical small intervals containing primes, arXiv:0908.2319 [math.NT], 2009.
V. Shevelev, Ramanujan and Labos Primes, Their Generalizations, and Classifications of Primes, J. Int. Seq. 15 (2012) # 12.5.4
J. Sondow, J. W. Nicholson, and T. D. Noe, Ramanujan Primes: Bounds, Runs, Twins, and Gaps, arXiv:1105.2249 [math.NT], 2011; J. Integer Seq. 14 (2011) Article 11.6.2.

Cf. A080359, A104272, A164288, A164294, A164332, A001262, A001567, A062568, A141232.
Cf. A164368, A164554, A166251, A166252. [Vladimir Shevelev, Oct 10 2009]
Cf. A166307, A182365.

isA164333 := proc(n)
        local i ;
        if isprime(n) and n > 3 then
                for i from (prevprime(n)+1)/2 to (n-1)/2 do
                        if isprime(i) then
                                return false;
                        end if;
                end do;
                return true;
        else
                false;
        end if;
end proc:
for i from 2 to 700 do
        if isA164333(i) then
                printf("%d,",i);
        end if;
end do: # R. J. Mathar, Oct 29 2011

kmax = 200; Select[Table[{(Prime[k - 1] + 1)/2, (Prime[k] - 1)/2}, {k, 3, kmax}], AllTrue[Range[#[[1]], #[[2]]], CompositeQ]&][[All, 2]]*2 + 1 (* Jean-François Alcover, Nov 14 2017 *)

{A080359} union {A164294} = {this sequence} union {2,3}. - Vladimir Shevelev, Oct 29 2011

A164368(2)A164368(3)A164368(4)Vladimir Shevelev, Oct 10 2009]

Definition rephrased by R. J. Mathar, Oct 02 2009

A020136 Fermat pseudoprimes to base 4.

Original entry on oeis.org

15, 85, 91, 341, 435, 451, 561, 645, 703, 1105, 1247, 1271, 1387, 1581, 1695, 1729, 1891, 1905, 2047, 2071, 2465, 2701, 2821, 3133, 3277, 3367, 3683, 4033, 4369, 4371, 4681, 4795, 4859, 5461, 5551, 6601, 6643, 7957, 8321, 8481, 8695, 8911, 9061, 9131

Offset: 1

David W. Wilson

nonn

If q and 2q-1 are odd primes, then n=q*(2q-1) is in the sequence. So for n>1, A005382(n)*(2*A005382(n)-1) form a subsequence (cf. A129521). - Farideh Firoozbakht, Sep 12 2006
Primes q and 2q-1 are a Cunningham chain of the second kind. - Walter Nissen, Sep 07 2009
Composite numbers n such that 4^(n-1) == 1 (mod n). - Michel Lagneau, Feb 18 2012

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)
Chris Caldwell, Cunningham chain.
Chris Caldwell et al., Top Twenty Cunningham Chains (2nd kind).
Eric Weisstein's World of Mathematics, Fermat Pseudoprime.
Index entries for sequences related to pseudoprimes

Subsequence of A122781.
Contains A001567 (Fermat pseudoprimes to base 2) as a subsequence.
Cf. A005382, A129521.

Select[Range[9200], ! PrimeQ[ # ] && PowerMod[4, # - 1, # ] == 1 &] (* Farideh Firoozbakht, Sep 12 2006 *)

isok(n) = (Mod(4, n)^(n-1)==1) && !isprime(n) && (n>1); \\ Michel Marcus, Apr 27 2018

cp's OEIS Frontend

A065341 Mersenne composites: 2^prime(m) - 1 is not a prime.

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A005936 Pseudoprimes to base 5.

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A007013 Catalan-Mersenne numbers: a(0) = 2; for n >= 0, a(n+1) = 2^a(n) - 1.

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A050217 Super-Poulet numbers: Poulet numbers whose divisors d all satisfy d|2^d-2.

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A005938 Pseudoprimes to base 7.

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A090086 Smallest pseudoprime to base n, not necessarily exceeding n (cf. A007535).

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A122780 Nonprimes k such that 3^k == 3 (mod k).

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