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A052214 Numbers n with prime signature(n) = prime signature(n+1) = prime signature(n+2). 9
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A subsequence of A005238. - M. F. Hasler, Jan 05 2013

LINKS

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

EXAMPLE

33 = 3^1 11^1, 34 = 2^1 17^1 and 35 = 5^1 7^1, so all have prime signature {1,1}.

MATHEMATICA

pri[ n_ ] := Sort[ Transpose[ FactorInteger[ n ] ][ [ 2 ] ] ] Select[ Range[ 2, 10000 ], pri[ # ]==pri[ #+1 ]==pri[ #+2 ]& ]

PROG

(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

CROSSREFS

Cf. A075039.

Sequence in context: A056809 A073251 A005238 * A063838 A075039 A039833

Adjacent sequences:  A052211 A052212 A052213 * A052215 A052216 A052217

KEYWORD

easy,nonn

AUTHOR

Erich Friedman, Jan 29 2000

STATUS

approved

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Last modified July 30 23:15 EDT 2014. Contains 245076 sequences.