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A330508
Numbers k such that k + 6^t is semiprime for t = 0 to 9.
1
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.
Sequence in context: A251826 A237461 A215599 * A204395 A181261 A237013
KEYWORD
nonn
AUTHOR
K. D. Bajpai, Dec 16 2019
STATUS
approved