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Prime nearest to 2^n. In case of a tie, choose the larger.
2

%I #17 Feb 19 2023 15:10:48

%S 2,2,5,7,17,31,67,127,257,509,1021,2053,4099,8191,16381,32771,65537,

%T 131071,262147,524287,1048573,2097143,4194301,8388617,16777213,

%U 33554467,67108859,134217757,268435459,536870909,1073741827,2147483647,4294967291,8589934583

%N Prime nearest to 2^n. In case of a tie, choose the larger.

%H Harvey P. Dale, <a href="/A356434/b356434.txt">Table of n, a(n) for n = 0..1000</a>

%F a(0) = 2; for n >= 1, if A014210(n) + A014234(n) > 2^(n+1) then a(n) = A014234(n), otherwise a(n) = A014210(n).

%t Join[{2,2},Table[Max[Nearest[{NextPrime[2^n,-1],NextPrime[2^n]},2^n]],{n,2,40}]] (* _Harvey P. Dale_, Feb 19 2023 *)

%o (Python)

%o from sympy import prevprime, nextprime

%o def A356434(n): return (r if (m:=nextprime(k:=1<<n)) > (k<<1)-(r:=prevprime(k)) else m) if n>1 else 2 # _Chai Wah Wu_, Aug 08 2022

%Y A117387 differs by preferring the smaller prime in the case of a tie, which occurs when n is in A226178.

%Y Cf. A014210, A014234, A340707.

%K nonn

%O 0,1

%A _Peter Munn_, Aug 07 2022