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A016041 Primes that are palindromic in base 2 (but written here in base 10). 27
3, 5, 7, 17, 31, 73, 107, 127, 257, 313, 443, 1193, 1453, 1571, 1619, 1787, 1831, 1879, 4889, 5113, 5189, 5557, 5869, 5981, 6211, 6827, 7607, 7759, 7919, 8191, 17377, 18097, 18289, 19433, 19609, 19801, 21157, 22541, 22669, 22861, 23581, 24029 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A002385 for palindromic primes in base 10, and A256081 for primes whose binary expansion is "balanced" (see there) but not palindromic. - M. F. Hasler, Mar 14 2015

LINKS

Zak Seidov and Michael De Vlieger, Table of n, a(n) for n = 1..3000 (first 1000 terms by Zak Seidov)

K. S. Brown, On General Palindromic Numbers

P. De Geest, World!Of Palindromic Primes

MATHEMATICA

lst = {}; Do[ If[ PrimeQ@n, t = IntegerDigits[n, 2]; If[ FromDigits@t == FromDigits@ Reverse@ t, AppendTo[lst, n]]], {n, 3, 50000, 2}]; lst

pal2Q[n_] := Reverse[x = IntegerDigits[n, 2]] == x; Select[Prime[Range[2800]], pal2Q[#] &] (* Jayanta Basu, Jun 23 2013 *)

CROSSREFS

Intersection of A000040 & A006995. First row of A095749. A095741 gives the number of terms in range [2^(2n), 2^(2n+1)]. Cf. A095730 for primes whose Zeckendorf-expansion is palindromic and A029971 for those whose ternary (base-3) expansion is.

Cf. A117697 (written in base 2), A002385, A256081.

Sequence in context: A274906 A174394 A057476 * A140797 A245730 A038893

Adjacent sequences:  A016038 A016039 A016040 * A016042 A016043 A016044

KEYWORD

nonn,easy,base

AUTHOR

Robert G. Wilson v

EXTENSIONS

More terms from Patrick De Geest.

Syntax of the Mathematica coding corrected by Robert G. Wilson v, Aug 10 2009

STATUS

approved

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Last modified March 24 06:12 EDT 2017. Contains 283984 sequences.