

A281551


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


1



3, 23, 41, 47, 59, 89, 101, 149, 179, 227, 317, 347, 353, 383, 389, 479, 503, 599, 821, 887, 929, 977, 1019, 1109, 1229, 1283, 1319, 1511, 1571, 1619, 1667, 1709, 1733, 1787, 1847, 1889, 1907, 1913, 1931, 2207, 2309, 2333, 2357, 2399, 2417, 2459, 2609, 2753, 2789, 2909, 2963, 2999, 3203, 3257, 3299
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OFFSET

1,1


LINKS

Indranil Ghosh, Table of n, a(n) for n = 1..2014


EXAMPLE

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


PROG

(Python)
import math
from sympy import isprime
def unary(n):
....return "1"*(n1)+"0"
def elias_gamma(n):
....if n ==1:
........return "1"
....k=int(math.log(n, 2))
....fp=unary(1+k) #fp is the first part
....sp=n2**(k) #sp is the second part
....nb=k #nb is the number of bits used to store sp in binary
....sp=bin(sp)[2:]
....if len(sp)<nb:
........sp=("0"*(nblen(sp)))+sp
....return int(fp+sp, 2)
i=1
j=1
while j<=2014:
....if isprime(i)==True and isprime(elias_gamma(i))==True:
........print str(j)+" "+str(i)
........j+=1
....i+=1


CROSSREFS

Cf. A000040, A171885 (decimal representation of Elias gamma code), A281149, A281316.
Sequence in context: A106892 A116893 A106066 * A167216 A309935 A212396
Adjacent sequences: A281548 A281549 A281550 * A281552 A281553 A281554


KEYWORD

nonn,base


AUTHOR

Indranil Ghosh, Jan 24 2017


STATUS

approved



