A342443 - OEIS

%I #58 Dec 15 2024 20:16:31

%S 5,97,991,9949,99971,999983,9999991,99999989,999999937,9999999943,

%T 99999999977,999999999989,9999999999763,99999999999959,999999999999989

%N a(n) is the largest prime < 10^n that is the sum of at least two consecutive primes.

%C The minimum corresponding number of consecutive primes to get this largest prime a(n) is A342444(n) and the first prime of these A342444(n) consecutive primes is A342454(n).

%C Differs from A342439 where the corresponding primes result of the longest sum < 10^n of consecutive primes.

%C a(n) is the largest n-digit prime A003618(n) for n = 2, 6, 7, 8, 9, 11, 12, ...

%C a(13) >= k = 10^13 - 237. If a(13) > k then it is the sum of at least 30000 primes. k can be written as the sum of 6449 consecutive primes. - _David A. Corneth_, Mar 13 2021

%C No sum of 30000 or more consecutive primes is in the interval [10^13 - 237, 10^13 - 1], so a(13) = 10^13 - 237. - _Jon E. Schoenfield_, Mar 14 2021

%F A342439(n) <= a(n) <= A003618(n).

%e a(1) = 5 = 2 + 3, since it is not possible to obtain the greatest 1-digit prime 7 when adding consecutive primes.

%e a(2) = 29 + 31 + 37 = 97, since (29, 31, 37) are consecutive primes and 97 is the largest 2-digit prime.

%Y Cf. A003618, A050936, A067377, A342439, A342440, A342444, A342453, A342454.

%K nonn,base,more

%O 1,1

%A _Bernard Schott_, Mar 12 2021

%E a(9) from _Jinyuan Wang_, Mar 13 2021

%E a(10) from _David A. Corneth_, Mar 13 2021

%E a(11)-a(12) from _Jinyuan Wang_, Mar 13 2021

%E a(13)-a(14) from _Jon E. Schoenfield_, Mar 13 2021

%E a(15) from _Max Alekseyev_, Dec 11 2024