A058079 a(n) = p3, where {p1,p2,p3} are 3 consecutive primes with increasing order such that gcd(C(p3,p2), C(p2,p1)) = 1, where C is the binomial coefficient.

5, 7, 19, 23, 43, 73, 79, 107, 149, 151, 167, 173, 197, 199, 211, 271, 293, 313, 349, 367, 389, 409, 433, 439, 457, 467, 503, 509, 593, 619, 643, 647, 683, 773, 821, 823, 827, 863, 883, 887, 997, 1019, 1051, 1069, 1217, 1223

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

73 is here because C(73,71) = 2628 = 4*9*73 and C(71,67) = 971635 = 71*23*17*7*5 are relatively prime.

Mathematica

Select[Partition[Prime[Range[200]], 3, 1], GCD[Binomial[#[[3]], #[[2]]], Binomial[#[[2]], #[[1]]]]==1&][[;; , 3]] (* Harvey P. Dale, Feb 26 2023 *)

Prog

(PARI) is(n)=my(p=precprime(n-1), q=precprime(p-1)); gcd(binomial(n, p), binomial(p, q))==1 && isprime(n) && n>4 \\ Charles R Greathouse IV, Nov 13 2015

Crossrefs

Sequence in context: A258655 A174362 A268608 * A076787 A332763 A094963

Adjacent sequences: A058076 A058077 A058078 * A058080 A058081 A058082

Keyword

nonn

Author

Labos Elemer, Nov 13 2000

Extensions

Name corrected by Charles R Greathouse IV, Nov 13 2015

Status

approved