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 A100813 Smallest number in base 2 which is also prime in base 2+n, or 0 if no such number exists. 1

%I #13 Aug 20 2022 13:37:56

%S 10,11,10,11,10,111,1011,11,10,11,10,101,111,11,10,11,10,101,111,11,

%T 10,101,111011,101,111,11,10,11,10,1011,111,10001,1101,11,10,111,1011,

%U 11,10,11,10,1011,1101,11,10,1011,1100111,111,101001,11,10,101,111011,101

%N Smallest number in base 2 which is also prime in base 2+n, or 0 if no such number exists.

%H Michael S. Branicky, <a href="/A100813/b100813.txt">Table of n, a(n) for n = 1..10000</a>

%e a(6) = 111: 111 (base 2) = 7, which is prime; 111 (base 2+6) = 73, which is prime.

%t a = {}; Do[ k = 1; While[ ! PrimeQ[FromDigits[IntegerDigits[Prime[k], 2], 2 + n]], k++ ]; AppendTo[a, FromDigits[IntegerDigits[Prime[k], 2], 10]];, {n, 50}]; a (* _Ray Chandler_, Jan 10 2005 *)

%o (Python)

%o from sympy import isprime, nextprime

%o def fd(s, b): return sum(b**i for i, si in enumerate(s[::-1]) if si=='1')

%o def a(n):

%o p = 2

%o while not isprime(fd(bin(p)[2:], n+2)): p = nextprime(p)

%o return int(bin(p)[2:])

%o print([a(n) for n in range(1, 55)]) # _Michael S. Branicky_, Aug 20 2022

%K base,nonn

%O 1,1

%A _Ray G. Opao_, Jan 05 2005

%E Corrected and extended by _Ray Chandler_, Jan 10 2005

%E a(51) and beyond from _Michael S. Branicky_, Aug 09 2022

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Last modified June 15 03:12 EDT 2024. Contains 373402 sequences. (Running on oeis4.)