[go: up one dir, main page]

login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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