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A095741 Number of base-2 palindromic primes (A016041) in range ]2^2n,2^(2n+1)]. 5
2, 2, 3, 3, 7, 12, 23, 40, 94, 142, 271, 480, 856, 1721, 3099, 5572, 10799, 20782, 39468, 72672, 139867, 274480, 520376, 986318, 1914097, 3726617, 7107443, 13682325, 26430797, 51412565, 99204128, 190457946 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Note that there are no such primes in any range ]2^(2n-1),2^2n], as all even-length binary palindromes are divisible by 3 (cf. A048702).

The ratio a(n)/A036378(2n) converges as follows: 1, 0.4, 0.230769, 0.069767, 0.051095, 0.025862, 0.014268, 0.007006, 0.00461, 0.00193, 0.00101, 0.000487, 0.000235, 0.000127, 0.000061, 0.000029

LINKS

Table of n, a(n) for n=1..32.

A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence

Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]

MATHEMATICA

palindromicQ[n_, b_:10] := TrueQ[IntegerDigits[n, b] == Reverse[IntegerDigits[n, b]]]; Table[Length[Select[Range[2^(2n), 2^(2n + 1)], palindromicQ[#, 2] && PrimeQ[#] &]], {n, 10}] (* Alonso del Arte, Jan 13 2012 *)

PROG

(PARI) m=vector(65536); u=vector(#m); u[1]=1; for(b=1, #m-1, c=b; e=2^floor(log(b+.5)/log(2)); d=0; u[b+1]=e; while(c>0, d=d+e*(c%2); c=floor(c/2); e=e/2); m[b+1]=d); for(x=0, 31, h=0; y=2^x; for(w=y, 2*y-1, if(x<16, v1=4*y*w+m[w+1]; v2=v1+2*y, w1=floor(w/65536); w2=w-65536*w1; v1=262144*y*w1+4*y*w2+65536*u[w1+1]/u[w2+1]*m[w2+1]+m[w1+1]; v2=v1+2*y); if(isprime(v1), h++); if(isprime(v2), h++)); print(2*x+3" bits: "h)) \\ Martin Raab, Jan 13 2012

CROSSREFS

Bisection of the first diagonal of triangle A095759. Cf. also A095731.

Sequence in context: A032060 A241385 A153903 * A252582 A181577 A110880

Adjacent sequences:  A095738 A095739 A095740 * A095742 A095743 A095744

KEYWORD

nonn,base,more

AUTHOR

Antti Karttunen, Jun 12 2004

EXTENSIONS

a(27), ..., a(32) from Martin Raab, Oct 20 2015

STATUS

approved

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Last modified December 13 14:58 EST 2017. Contains 295958 sequences.