A092250 - OEIS

%I #38 Jan 18 2022 02:30:07

%S 5,71,881,9929,99989,999959,9999971,99999587,999999191,9999999701,

%T 99999999761,999999999959,9999999998489,99999999999971,

%U 999999999997967,9999999999999641,99999999999998807,999999999999998927

%N Lesser of the greatest twin prime pair with n digits.

%C Sum of reciprocals = 0.215331408...

%C Also the numerator of the largest prime-over-prime fraction less than 1 that is the ratio of two primes both less than 10^n. - _Cino Hilliard_, Feb 13 2006 [edited by _Jon E. Schoenfield_, Dec 01 2019]

%H Robert G. Wilson v, <a href="/A092250/b092250.txt">Table of n, a(n) for n = 1..1000</a>

%H Robert G. Wilson v, <a href="/A092250/a092250.txt">Table of n, a(n) for n = 1..1250 (includes terms with more than 1000 digits)</a>

%t Array[Block[{k = 10^# - 3}, While[! AllTrue[{k, k + 2}, PrimeQ], k -= 2]; k] &, 18]

%o (PARI) lasttwpr(n) = { sr=0; for(m=0,n, c=0; forstep(x=10^(m+1)-1,10^m,-2, if(isprime(x)&& isprime(x-2),print1(x-2",");sr+=1./(x-2);break) ) ); print(); print(sr) }

%o (PARI) apply( {A092250(n,p=10^n)=until(2==p-p=precprime(p-1),);p}, [1..22]) \\ avoids multiple isprime(): much faster! - _M. F. Hasler_, Jan 17 2022

%o (Python)

%o from sympy import prevprime

%o def a(n):

%o     p = prevprime(10**n); pp = prevprime(p)

%o     while p - pp != 2: p, pp = pp, prevprime(pp)

%o     return pp

%o print([a(n) for n in range(1, 19)]) # _Michael S. Branicky_, Jan 17 2022

%Y Cf. A092245.

%Y Cf. A114429(n) = a(n)+2: largest twin prime < 10^n.

%K base,nonn

%O 1,1

%A _Cino Hilliard_, Feb 17 2004