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

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

Offset: 1

Author

Erich Friedman, Jan 29 2000

Keywords

• easy
• nonn

Examples

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

Links

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

Crossrefs

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

Cf. A075039.

Programs

Mathematica

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

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