A330508 Numbers k such that k + 6^t is semiprime for t = 0 to 9.

61273, 109441, 160213, 274501, 275473, 311593, 360673, 394201, 477181, 486061, 514993, 522085, 617137, 620053, 715477, 725485, 803833, 812677, 847117, 1063585, 1146913, 1182577, 1215865, 1232917, 1409425, 1508113, 1587241, 1768993, 1863073, 1895413, 2085517, 2095177

Offset

1,1

Comments

a(2620) = 530079693 is the first multiple of 3 in this sequence; there are no multiples of 2. - Charles R Greathouse IV, Dec 20 2019

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

a(1) = 61273:
  61273 + 6^0  =    61274 =   2 *  30637;
  61273 + 6^1  =    61279 = 233 *    263;
  61273 + 6^2  =    61309 =  37 *   1657;
  61273 + 6^3  =    61489 =  17 *   3617;
  61273 + 6^4  =    62569 =  13 *   4813;
  61273 + 6^5  =    69049 =  29 *   2381;
  61273 + 6^6  =   107929 =  37 *   2917;
  61273 + 6^7  =   341209 =  11 *  31019;
  61273 + 6^8  =  1740889 = 197 *   8837;
  61273 + 6^9  = 10138969 =  89 * 113921;
all ten results are semiprime.

Mathematica

fX[n_] = PrimeOmega[n] == 2; Select[Range[2000000], AllTrue[# + 6^{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, fX] &]

Prog

(Magma) f:=func<n|&+[d[2]: d in Factorization(n)] eq 2>; [k:k in [1..2100000]|forall{m:m in [0..9]|f(k+6^m)}]; // Marius A. Burtea, Dec 20 2019
(PARI) issemi(n)=bigomega(n)==2
is(n)=for(t=0, 9, if(!issemi(n+6^t), return(0))); 1 \\ Charles R Greathouse IV, Dec 20 2019

Crossrefs

Subsequence of A076274.

Cf. A001358, A082919, A096173, A104238, A105041.

Sequence in context: A251826 A237461 A215599 * A204395 A181261 A237013

Adjacent sequences: A330505 A330506 A330507 * A330509 A330510 A330511

Keyword

nonn

Author

K. D. Bajpai, Dec 16 2019

Status

approved