A140292 - OEIS

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

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..57.

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 *)

CROSSREFS

Cf. A001358, A034794, A088190.

Sequence in context: A178241 A028839 A141833 * A208980 A010426 A243170

Adjacent sequences: A140289 A140290 A140291 * A140293 A140294 A140295

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, May 24 2008

EXTENSIONS

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

STATUS

approved