A135785 - OEIS

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A135785

Union of A000040, A001248 and A037074.

2, 3, 4, 5, 7, 9, 11, 13, 15, 17, 19, 23, 25, 29, 31, 35, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 143, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241

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OFFSET

1,1

COMMENTS

a(n) possesses the following property: every i not exceeding a(n)/2 for which (a(n),i)>1 does not divide binomial(a(n)-i-1,i-1). Numbers with this property are called "binomial primes". There exist only nine binomial primes which are not terms of this sequence:1,6,8,10,12,20,21,24,33.

LINKS

Table of n, a(n) for n=1..62.

V. Shevelev, On divisibility of binomial(n-i-1,i-1) by i, Int. J. of Number Theory, 3, no.1 (2007), 119-139.

MATHEMATICA

aQ[n_] := PrimeQ[n] || (PrimeNu[n]<3 && Module[{p = FactorInteger[n][[1, 1]]}, n==p^2 || (n==p(p+2) && PrimeQ[p+2])]); Select[Range[2, 250], aQ] (* Amiram Eldar, Dec 04 2018 *)

PROG

(PARI) isok(n) = isprime(n) || (issquare(n) && isprime(sqrtint(n))) || (issquare(n+1) && isprime(sqrtint(n+1)-1) && isprime(sqrtint(n+1)+1)); \\ Michel Marcus, Dec 04 2018

CROSSREFS

Cf. A138389, A000040, A001248, A037074.

Sequence in context: A024926 A051532 A325461 * A262249 A248421 A008732

Adjacent sequences: A135782 A135783 A135784 * A135786 A135787 A135788

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, May 10 2008, May 16 2008

EXTENSIONS

Missing 47 and more terms from Michel Marcus, Dec 04 2018

STATUS

approved