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A052214
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Numbers n with prime signature(n) = prime signature(n+1) = prime signature(n+2).
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12
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33, 85, 93, 141, 201, 213, 217, 301, 393, 445, 603, 633, 697, 921, 1041, 1137, 1261, 1274, 1309, 1345, 1401, 1641, 1761, 1837, 1885, 1893, 1924, 1941, 1981, 2013, 2101, 2181, 2217, 2305, 2361, 2433, 2461, 2517, 2523, 2641, 2665, 2721, 2733, 3097, 3385
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OFFSET
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1,1
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LINKS
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EXAMPLE
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33 = 3^1 11^1, 34 = 2^1 17^1 and 35 = 5^1 7^1, so all have prime signature {1,1}.
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MATHEMATICA
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pri[ n_ ] := Sort[ Transpose[ FactorInteger[ n ] ][ [ 2 ] ] ] Select[ Range[ 2, 10000 ], pri[ # ]==pri[ #+1 ]==pri[ #+2 ]& ]
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PROG
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(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
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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