login
A083792
Lexicographically first increasing sequence such that no two successive terms have the same prime signature.
2
1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 36, 37, 38, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 77, 78, 79, 80, 81
OFFSET
1,2
LINKS
EXAMPLE
From Jon E. Schoenfield, Aug 13 2017: (Start)
a(1) = 1 (which has no prime factors);
a(2) = 2 (a prime);
a(3) cannot be 3, because 2 and 3 have the same prime signature (each is a prime); however, the prime signature of 4 (the square of a prime) differs from that of 2, so a(3) = 4. (End)
MAPLE
s:= n-> sort(map(i-> i[2], ifactors(n)[2])):
a:= proc(n) option remember; local k; for k from
1+a(n-1) while s(k)=s(a(n-1)) do od; k
end: a(1):=1:
seq(a(n), n=1..80); # Alois P. Heinz, Mar 09 2018
MATHEMATICA
{1, 2} ~Join~ Select[Range[2, 80], Last /@ FactorInteger[#] != Last /@ FactorInteger[# - 1] &] (* Giovanni Resta, Aug 14 2017 *)
CROSSREFS
Cf. A083793.
Sequence in context: A094798 A326178 A162880 * A083794 A133016 A026503
KEYWORD
easy,nonn
AUTHOR
Amarnath Murthy, May 07 2003
EXTENSIONS
More terms from James A. Sellers, May 19 2003
Incorrect term 76 removed by Alois P. Heinz, Mar 09 2018
STATUS
approved