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

1,1

Links

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

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

Adjacent sequences: A214517 A214518 A214519 * A214521 A214522 A214523

Keyword

nonn

Author

T. D. Noe, Aug 06 2012

Status

approved