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A052214 Numbers n with prime signature(n) = prime signature(n+1) = prime signature(n+2).

%I A052214 #17 Aug 29 2022 15:30:18
%S A052214 33,85,93,141,201,213,217,301,393,445,603,633,697,921,1041,1137,1261,
%T A052214 1274,1309,1345,1401,1641,1761,1837,1885,1893,1924,1941,1981,2013,
%U A052214 2101,2181,2217,2305,2361,2433,2461,2517,2523,2641,2665,2721,2733,3097,3385
%N A052214 Numbers n with prime signature(n) = prime signature(n+1) = prime signature(n+2).
%H A052214 Charles R Greathouse IV, <a href="/A052214/b052214.txt">Table of n, a(n) for n = 1..10000</a>
%e A052214 33 = 3^1 11^1, 34 = 2^1 17^1 and 35 = 5^1 7^1, so all have prime signature {1,1}.
%t A052214 pri[ n_ ] := Sort[ Transpose[ FactorInteger[ n ] ][ [ 2 ] ] ] Select[ Range[ 2,10000 ],pri[ # ]==pri[ #+1 ]==pri[ #+2 ]& ]
%o A052214 (PARI) A052214(n, /*give optional 2nd arg =1 to print all terms*/ show_all=0, a=2*3)={until( !n-- || !a++, until(, vecsort(factor(a+=2)[, 2])!=vecsort(factor(a-1)[, 2]) && next; ((t=vecsort(factor(a-1)[, 2]))==vecsort(factor(a-2)[, 2]) || vecsort(factor(a++)[, 2])==t) && (a-=2) && break); show_all && print1(a", ")); a}  \\ - _M. F. Hasler_, Jan 06 2013
%Y A052214 A subsequence of A005238. - _M. F. Hasler_, Jan 05 2013
%Y A052214 Cf. A075039.
%K A052214 easy,nonn
%O A052214 1,1
%A A052214 _Erich Friedman_, Jan 29 2000