A309289 Numbers k such that binomial(2k,k) - k^2 is prime.

2, 3, 5, 9, 13, 27, 47, 59, 111, 547, 923, 1301, 2263, 5189

Offset

1,1

Comments

If a term k > 2 is divisible by a prime p, then all digits in the base-p expansion of k are less than p/2. In particular, 2 is the only even term. - Robert Israel, Aug 02 2019

Links

Table of n, a(n) for n=1..14.

Juri-Stepan Gerasimov and others, C(2n,n) - n^2 and C(n^2,n) - n^n, SeqFan list, April 20, 2018.

Maple

filter:= t -> isprime(binomial(2*t, t)-t^2):
select(filter, [2, seq(i, i=3..6000, 2)]); # Robert Israel, Aug 02 2019

Prog

(PARI) is(n)=ispseudoprime(binomial(2*n, n)-n^2)
for(n=0, oo, is(n) && print1(n, ", "))

Crossrefs

Cf. A309290 (binomial(k^2,k) - k^2 is squarefree).

Sequence in context: A171925 A186946 A057225 * A220315 A070819 A195667

Adjacent sequences: A309286 A309287 A309288 * A309290 A309291 A309292

Keyword

nonn,hard,more

Author

M. F. Hasler (at the suggestion of Juri-Stepan Gerasimov and others), Jul 21 2019

Status

approved