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Prime numbers p such that the decimal representation of its Elias gamma code is also a prime.
1

%I #15 Jan 27 2017 13:13:37

%S 3,23,41,47,59,89,101,149,179,227,317,347,353,383,389,479,503,599,821,

%T 887,929,977,1019,1109,1229,1283,1319,1511,1571,1619,1667,1709,1733,

%U 1787,1847,1889,1907,1913,1931,2207,2309,2333,2357,2399,2417,2459,2609,2753,2789,2909,2963,2999,3203,3257,3299

%N Prime numbers p such that the decimal representation of its Elias gamma code is also a prime.

%H Indranil Ghosh, <a href="/A281551/b281551.txt">Table of n, a(n) for n = 1..2014</a>

%e 59 is in the sequence because the decimal representation of its Elias gamma code is 2011 and both 59 and 2011 are prime numbers.

%o (Python)

%o import math

%o from sympy import isprime

%o def unary(n):

%o ....return "1"*(n-1)+"0"

%o def elias_gamma(n):

%o ....if n ==1:

%o ........return "1"

%o ....k=int(math.log(n,2))

%o ....fp=unary(1+k) #fp is the first part

%o ....sp=n-2**(k) #sp is the second part

%o ....nb=k #nb is the number of bits used to store sp in binary

%o ....sp=bin(sp)[2:]

%o ....if len(sp)<nb:

%o ........sp=("0"*(nb-len(sp)))+sp

%o ....return int(fp+sp,2)

%o i=1

%o j=1

%o while j<=2014:

%o ....if isprime(i)==True and isprime(elias_gamma(i))==True:

%o ........print str(j)+" "+str(i)

%o ........j+=1

%o ....i+=1

%Y Cf. A000040, A171885 (decimal representation of Elias gamma code), A281149, A281316.

%K nonn,base

%O 1,1

%A _Indranil Ghosh_, Jan 24 2017