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A016041 Primes that are palindromic in base 2 (but written here in base 10). 32
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
Number of terms less than 4^k, k=0,1,2,...: 2, 4, 6, 9, 12, 19, 31, 54, 94, 188, 330, 601, 1081, 1937, 3658, 6757, 12329, 23128, 43910, 83378, 156050, 295917, 570397, 1090773, 2077091, 3991188, 7717805, 14825248, 28507573, 54938370, 106350935, ..., partial sums of A095741 plus 2. - Robert G. Wilson v, Feb 23 2018
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Zak Seidov, terms 1001..3000 from Michael De Vlieger)
Patrick De Geest, World!Of Palindromic Primes
FORMULA
Sum_{n>=1} 1/a(n) = A194097. - Amiram Eldar, Mar 19 2021
MATHEMATICA
lst = {}; Do[ If[ PrimeQ@n, t = IntegerDigits[n, 2]; If[ FromDigits@t == FromDigits@ Reverse@ t, AppendTo[lst, n]]], {n, 3, 50000, 2}]; lst (* syntax corrected by Robert G. Wilson v, Aug 10 2009 *)
pal2Q[n_] := Reverse[x = IntegerDigits[n, 2]] == x; Select[Prime[Range[2800]], pal2Q[#] &] (* Jayanta Basu, Jun 23 2013 *)
genPal[n_Integer, base_Integer: 10] := Block[{id = IntegerDigits[n, base], insert = Join[{{}}, {# - 1} & /@ Range[base]]}, FromDigits[#, base] & /@ (Join[id, #, Reverse@id] & /@ insert)]; k = 0; lst = {}; While[k < 100, AppendTo[lst, Select[ genPal[k, 2], PrimeQ]]; lst = Flatten@ lst; k++]; lst (* Robert G. Wilson v, Feb 23 2018 *)
PROG
(PARI) is(n)=isprime(n)&&Vecrev(n=binary(n))==n \\ M. F. Hasler, Feb 23 2018
(Magma) [NthPrime(n): n in [1..5000] | (Intseq(NthPrime(n), 2) eq Reverse(Intseq(NthPrime(n), 2)))]; // Vincenzo Librandi, Feb 24 2018
CROSSREFS
Intersection of A000040 and A006995.
First row of A095749.
A095741 gives the number of terms in range [2^(2n), 2^(2n+1)].
Cf. A095730 (primes whose Zeckendorf expansion is palindromic), A029971 (primes whose ternary (base-3) expansion is palindromic).
Cf. A117697 (written in base 2), A002385, A194097, A256081.
Sequence in context: A296422 A174394 A057476 * A140797 A245730 A038893
KEYWORD
nonn,easy,base
AUTHOR
EXTENSIONS
More terms from Patrick De Geest
STATUS
approved

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Last modified June 6 10:50 EDT 2023. Contains 363142 sequences. (Running on oeis4.)