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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..72.

FORMULA

a(n) = binomial((A000120(p) + A023416(p), A000120(p)), where p=prime(n). - R. J. Mathar, May 15 2010

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

Cf. A004676, A168324.

Sequence in context: A175126 A142884 A325365 * A219356 A142878 A299774

Adjacent sequences:  A177684 A177685 A177686 * A177688 A177689 A177690

KEYWORD

nonn,base

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

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Last modified February 17 15:32 EST 2020. Contains 331998 sequences. (Running on oeis4.)