A144062 a(1)=1; for n>1, a(n) = least integer > a(n-1) such that a(n)^2-a(n-1)^2 = semiprime

1, 4, 5, 8, 11, 18, 23, 30, 37, 42, 43, 44, 57, 58, 69, 80, 81, 86, 93, 94, 97, 100, 101, 102, 103, 108, 109, 110, 111, 116, 123, 124, 125, 132, 133, 134, 137, 140, 143, 144, 145, 146, 165, 172, 175, 178, 181, 186, 193, 196, 197, 198, 203, 204, 215, 218, 219

Offset

1,2

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

2^2-1=3, not semiprime; 3^2-1=8, not semiprime; 4^2-1=15=3*5, semiprime, hence a(2)=4.

Mathematica

sp[n_]:=Module[{k=n+1}, While[PrimeOmega[k^2-n^2]!=2, k++]; k]; NestList[ sp, 1, 60] (* Harvey P. Dale, Oct 18 2016 *)

Prog

(PARI) lista(nn) = {cura = 1; print1(cura, ", "); for (n=1, nn, nexta = cura + 1; while (bigomega(nexta^2-cura^2) != 2, nexta++); cura = nexta; print1(nexta, ", "); ); } \\ Michel Marcus, Feb 28 2014

Crossrefs

Cf. A001358.

Sequence in context: A354937 A256535 A249669 * A066233 A130814 A183181

Adjacent sequences: A144059 A144060 A144061 * A144063 A144064 A144065

Keyword

easy,nonn

Author

Philippe Lallouet (philip.lallouet(AT)orange.fr), Sep 09 2008

Extensions

Corrected and extended by Michel Marcus, Feb 28 2014

Status

approved