A078830 -id:A078830 - cp's OEIS frontend

A078829 Numbers having exactly one prime contained as binary substring in binary representation of n.

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

Offset: 1

Reinhard Zumkeller, Dec 08 2002

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

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

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

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

Cf. A078826, A078830, A007088.

Cf. A225243.

a078829 n = a078829_list !! (n-1)
a078829_list = filter ((== 1) . a078826) [1..]
-- Reinhard Zumkeller, Jul 17 2015

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-François Alcover, May 23 2013 *)

A078831 Numbers n with unique occurrence of all binary substrings representing primes in binary representation of n.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 13, 16, 17, 19, 24, 25, 32, 33, 35, 48, 49, 64, 65, 67, 96, 97, 128, 129, 131, 192, 193, 256, 257, 259, 384, 385, 512, 513, 515, 768, 769, 1024, 1025, 1027, 1536, 1537, 2048, 2049, 2051, 3072, 3073, 4096, 4097, 4099, 6144, 6145

Offset: 1

Reinhard Zumkeller, Dec 08 2002

A078826(a(n)) = A078827(a(n)); A078830 is a subsequence.

			n=12 -> '1100' contains two substrings representing distinct primes: '10'=2 and '11'=3, therefore 12 is a term.

Ray Chandler, Table of n, a(n) for n = 1..110

Cf. A078826, A078827, A078830, A007088.

Extended by Ray Chandler, Nov 03 2008

cp's OEIS Frontend

A078829 Numbers having exactly one prime contained as binary substring in binary representation of n.

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