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A246131 Composite numbers such that c(a(n))-2 = 0 mod a(n), with c(m) being either the central binomial coefficient or the Catalan number. 2
4, 9, 25, 49, 121, 125, 169, 289, 343, 361, 418, 529, 841, 961, 1331, 1369, 1681, 1849, 2197, 2209, 2809, 3481, 3721, 4489, 4913, 5041, 5329, 6241, 6859, 6889, 7921, 9409, 10201, 10609, 11449, 11881, 12167, 12769, 16129, 17161, 18769, 19321, 22201, 22801, 24389, 24649, 26569, 27173 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A246130 for introductory comments. The values of s(m)=c(m)-2 are divisible by m whenever m is a prime. However, s(m) is also divisible by some composite numbers which, somewhat like Sarrus numbers (A001567) for the sequence 2^(m-1)-1, might be called the pseudoprimes of s(m). These, listed here, are initially more frequent than Sarrus numbers but their density eventually drops down faster.

By definition a supersequence of A082180. - R. J. Mathar, Sep 22 2014

LINKS

Stanislav Sykora, Table of n, a(n) for n = 1..140

MAPLE

select(n -> not isprime(n) and coeff(Power(1+x, 2*n) mod n, x, n) = 2, [$4 .. 10000]); # Robert Israel, Sep 22 2014

PROG

(PARI) a(file, nmax)={my(n=0, p=1);

  while(1, p++; if(((binomial(2*p, p)-2)%p)==0,

    if(!isprime(p), n++; write(file, n, " ", p); if(n==nmax, break)));

    if(p%1000==0, print(p)); \\ monitor progress

  ); }

CROSSREFS

Cf. A000108, A000984, A001567, A246130, A246132, A246133, A246134.

Sequence in context: A247136 A158145 A082180 * A068999 A179707 A247078

Adjacent sequences:  A246128 A246129 A246130 * A246132 A246133 A246134

KEYWORD

nonn

AUTHOR

Stanislav Sykora, Aug 16 2014

STATUS

approved

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Last modified July 26 08:24 EDT 2017. Contains 289799 sequences.