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A078829 Numbers having exactly one prime contained as binary substring in binary representation of n. 2
2, 3, 4, 8, 9, 16, 18, 32, 33, 36, 64, 65, 66, 72, 128, 129, 130, 132, 144, 256, 258, 260, 264, 265, 288, 289, 512, 513, 516, 520, 528, 530, 576, 578, 1024, 1025, 1026, 1032, 1040, 1056, 1057, 1060, 1152, 1156, 2048, 2049, 2050, 2052, 2064, 2080, 2112, 2114 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A078826(a(n)) = 1; A078830 is a subsequence;

for k>2 also floor(a(k)/2) belongs to the sequence.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..120

EXAMPLE

n=18 -> '10010' contains only 1 distinct binary substring which is prime: '10' (10bbb or bbb10), therefore 18 is a term.

MATHEMATICA

primeCount[n_] := (bits = IntegerDigits[n, 2]; lg = Length[bits]; Reap[Do[If[PrimeQ[p = FromDigits[bits[[i ;; j]], 2]], Sow[p]], {i, 1, lg-1}, {j, i+1, lg}]][[2, 1]] // Union // Length); primeCount[1] = 0; Select[Range[3000], primeCount[#] == 1 &] (* Jean-Fran├žois Alcover, May 23 2013 *)

PROG

(Haskell)

a078829 n = a078829_list !! (n-1)

a078829_list = filter ((== 1) . a078826) [1..]

-- Reinhard Zumkeller, Jul 17 2015

CROSSREFS

Cf. A078826, A078830, A007088.

Cf. A225243.

Sequence in context: A231811 A015922 A212255 * A045583 A045608 A068317

Adjacent sequences:  A078826 A078827 A078828 * A078830 A078831 A078832

KEYWORD

nonn,base,nice

AUTHOR

Reinhard Zumkeller, Dec 08 2002

STATUS

approved

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Last modified February 23 00:28 EST 2020. Contains 332157 sequences. (Running on oeis4.)