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

1,1

Comments

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

Links

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

Example

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.

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 *)

Crossrefs

Cf. A046933, A209619.

Sequence in context: A050967 A071382 A290450 * A031928 A095649 A016067

Adjacent sequences: A209615 A209616 A209617 * A209619 A209620 A209621

Keyword

nonn

Author

Lekraj Beedassy, Mar 21 2012

Status

approved