

A144753


A positive integer n is included if n is a palindrome in binary and n has a prime number of 1's in its binary representation.


2



3, 5, 7, 9, 17, 21, 31, 33, 65, 73, 93, 107, 127, 129, 257, 273, 313, 341, 381, 403, 443, 471, 513, 1025, 1057, 1137, 1193, 1273, 1317, 1397, 1453, 1571, 1651, 1707, 1831, 2047, 2049, 4097, 4161, 4321, 4433, 4593, 4681, 4841, 4953, 5189, 5349, 5461, 5709
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OFFSET

1,1


COMMENTS

Each term of this sequence is in both A006995 and A052294.


LINKS

Indranil Ghosh, Table of n, a(n) for n = 1..11167 (terms 1..1000 from Vincenzo Librandi)


EXAMPLE

21 in binary is 10101. This binary representation is a palindrome, it contains three 1's, and three is a prime. So 21 is included in the sequence.


MATHEMATICA

okQ[n_] := Module[{idn2 = IntegerDigits[n, 2]}, (idn2 == Reverse[idn2]) && PrimeQ[First[DigitCount[n, 2]]]]; Select[Range[10000], okQ] (* Harvey P. Dale, Sep 23 2008 *)


CROSSREFS

Cf. A144752, A006995, A052294.
Sequence in context: A146556 A084229 A191356 * A220221 A212292 A270837
Adjacent sequences: A144750 A144751 A144752 * A144754 A144755 A144756


KEYWORD

base,nonn


AUTHOR

Leroy Quet, Sep 20 2008


EXTENSIONS

More terms from Harvey P. Dale, Sep 23 2008


STATUS

approved



