A209618 Primes separated from their adjacent next primes by a composite number of successive composites.

139, 181, 241, 283, 337, 409, 421, 547, 577, 631, 691, 709, 787, 811, 829, 919, 1021, 1039, 1051, 1129, 1153, 1171, 1249, 1327, 1399, 1471, 1627, 1699, 1723, 1801, 1831, 1879, 1933, 1951, 2017, 2029, 2053, 2089, 2113, 2143, 2221, 2251, 2311, 2477, 2521, 2557

Offset: 1

Author

Lekraj Beedassy, Mar 21 2012

Keywords

• nonn

Comments

Primes prime(k) such that A046933(k) is composite. - Robert Israel, Jan 08 2025

Examples

			a(1) = 139 is the first prime separated from the next prime (149) by a composite number (9) of successive composites, namely, 140, 141, 142, 143, 144, 145, 146, 147, 148.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A046933, A209619.

Programs

Maple

P:= select(isprime,[seq(i,i=3..3000,2)]):
G:= P[2..-1]-P[1..-2]-~1:
J:= remove(t -> G[t]=1 or G[t]::prime, [$1..nops(G)]):
P[J]; # Robert Israel, Jan 08 2025

Mathematica

ps = Prime[Range[500]]; pos = Position[Differences[ps] - 1, ?(# > 1 && ! PrimeQ[#] &)]; ps[[Flatten[pos]]] (* _T. D. Noe, Mar 21 2012 *)