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A177687
Number of distinct transpositions of digits (zeros and units) in n-th prime written in base 2.
5
2, 1, 3, 1, 4, 4, 10, 10, 5, 5, 1, 20, 20, 15, 6, 15, 6, 6, 35, 35, 35, 21, 35, 35, 35, 35, 21, 21, 21, 35, 1, 56, 56, 70, 70, 56, 56, 70, 56, 56, 56, 56, 8, 56, 70, 56, 56, 8, 56, 56, 56, 8, 56, 8, 36, 126, 126, 126, 126, 126, 126, 126, 126, 84, 126, 84, 126, 126, 84, 84, 126, 84
OFFSET
1,1
LINKS
FORMULA
a(n) = binomial(A000120(p) + A023416(p), A000120(p)), where p=prime(n). - R. J. Mathar, May 15 2010
a(n) = A178244(A000040(n)). - Robert Israel, Oct 25 2023
EXAMPLE
a(1)=2 because 2 = 10_2 and |{10, 01}| = 2,
a(2)=1 because 3 = 11_2 and |{11}| = 1,
a(3)=3 because 5 = 101_2 and |{101, 011, 110}| = 3.
MAPLE
A177687 := proc(n) p := ithprime(n) ; combinat[numbperm](convert(p, base, 2)) ; end proc: seq(A177687(n), n=1..120) ; # R. J. Mathar, May 15 2010
MATHEMATICA
Array[Length@ Permutations@ IntegerDigits[Prime@ #, 2] &, 72] (* Michael De Vlieger, Feb 15 2019 *)
CROSSREFS
KEYWORD
nonn,base,look,easy
AUTHOR
Juri-Stepan Gerasimov, May 12 2010, May 14 2010
EXTENSIONS
Terms corrected by D. S. McNeil and R. J. Mathar, May 14 2010
STATUS
approved