A214520 Primes that are the only prime between consecutive semiprimes.

5, 7, 23, 37, 47, 53, 67, 79, 83, 89, 113, 127, 131, 157, 163, 167, 173, 211, 223, 251, 257, 263, 277, 293, 307, 317, 331, 337, 359, 367, 373, 379, 383, 389, 397, 401, 409, 449, 457, 467, 479, 487, 491, 499, 503, 509, 541, 547, 557, 563, 577, 587, 593, 613, 631

Offset: 1

Author

T. D. Noe, Aug 06 2012

Keywords

• nonn

Examples

			23 is the only prime between semiprimes 22 and 25.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358 (semiprimes).

Cf. A088701 (n primes between semiprimes).

Programs

Mathematica

SemiPrimeQ[n_Integer] := If[Abs[n] < 2, False, (2 == Plus @@ Transpose[FactorInteger[Abs[n]]][[2]])]; t = Select[Range[1000], SemiPrimeQ[#] &]; t2 = Select[Range[Length[t] - 1], PrimePi[t[[# + 1]]] - PrimePi[t[[#]]] == 1 &]; NextPrime[t[[t2]]]
Transpose[Select[{NextPrime[#[[1]]],NextPrime[#[[2]],-1]}&/@ Partition[ Select[ Range[700],PrimeOmega[#]==2&],2,1],Length[Union[#]]==1&]][[1]] (* Harvey P. Dale, Sep 01 2015 *)

Perl

use ntheory ":all"; my($i,$l)=(0,4); forsemiprimes { my $n=next_prime($l); print ++$i," $n\n" if $n < $ && next_prime($n) > $; $l=$;} 6,257; # _Dana Jacobsen, Mar 04 2019