A281551 Prime numbers p such that the decimal representation of its Elias gamma code is also a prime.

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

Offset: 1

Author

Indranil Ghosh, Jan 24 2017

Keywords

• nonn
• base

Examples

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

Links

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

Crossrefs

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

Programs

Python

import math
from sympy import isprime
def unary(n):
    return "1"*(n-1)+"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=n-2**(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)