A140292 a(n) is a square mod a(n-1), a(n) > a(n-1) and a(n) semiprime.

4, 9, 10, 14, 15, 21, 22, 25, 26, 35, 39, 49, 51, 55, 69, 82, 86, 87, 91, 95, 106, 115, 119, 121, 122, 123, 133, 134, 143, 146, 155, 159, 166, 169, 178, 183, 187, 202, 203, 219, 235, 249, 253, 254, 262, 265, 274, 278, 287, 289, 291, 295, 299, 302, 303, 309, 327

Offset: 1

Author

Jonathan Vos Post, May 24 2008

Keywords

• easy
• nonn

Crossrefs

Cf. A001358, A034794, A088190.

Programs

Maple

isqResid := proc(n,modp) local x ; for x from 1 to floor(modp/2) do if x^2 mod modp = n mod modp then RETURN(true) ; fi ; od: RETURN(false) ; end: isA001358 := proc(n) RETURN( numtheory[bigomega](n)= 2) ; end: A140292 := proc(n) option remember ; local a; if n = 1 then 4; else for a from A140292(n-1)+1 do if isA001358(a) and isqResid(a,A140292(n-1)) then RETURN(a) ; fi ; od ; fi ; end: seq(A140292(n),n=1..80) ; # R. J. Mathar, May 31 2008

Mathematica

quadResQ[n_, p_] := Module[{x}, For[x = 1, x <= Floor[p/2], x++, If[Mod[x^2, p] == Mod[n, p], Return[True]]]; Return[False]];
semiprimeQ[n_] := PrimeOmega[n] == 2;
a[n_] := a[n] = Module[{k}, If[n == 1, 4, For[k = a[n - 1] + 1, True, k++, If[semiprimeQ[k] && quadResQ[k, a[n - 1]], Return[k]]]]];
Table[a[n], {n, 1, 80}] (* Jean-François Alcover, Jan 28 2024, after R. J. Mathar *)

Extensions

Corrected and extended by R. J. Mathar, May 31 2008