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A214520
Primes that are the only prime between consecutive semiprimes.
3
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
1,1
EXAMPLE
23 is the only prime between semiprimes 22 and 25.
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 *)
PROG
(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
CROSSREFS
Cf. A001358 (semiprimes).
Cf. A088701 (n primes between semiprimes).
Sequence in context: A105890 A329625 A018656 * A156123 A288908 A166251
KEYWORD
nonn
AUTHOR
T. D. Noe, Aug 06 2012
STATUS
approved