A342443 a(n) is the largest prime < 10^n that is the sum of at least two consecutive primes.

5, 97, 991, 9949, 99971, 999983, 9999991, 99999989, 999999937, 9999999943, 99999999977, 999999999989, 9999999999763, 99999999999959

Offset

1,1

Comments

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).

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

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

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

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

Links

Table of n, a(n) for n=1..14.

Formula

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

Example

a(1) = 5 = 2 + 3, since it is not possible to obtain the greatest 1-digit prime 7 when adding consecutive primes.
a(2) = 29 + 31 + 37 = 97, since (29, 31, 37) are consecutive primes and 97 is the largest 2-digit prime.

Crossrefs

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

Sequence in context: A139950 A102734 A350516 * A117341 A295190 A202516

Adjacent sequences: A342440 A342441 A342442 * A342444 A342445 A342446

Keyword

nonn,base,more

Author

Bernard Schott, Mar 12 2021

Extensions

a(9) from Jinyuan Wang, Mar 13 2021

a(10) from David A. Corneth, Mar 13 2021

a(11)-a(12) from Jinyuan Wang, Mar 13 2021

a(13)-a(14) from Jon E. Schoenfield, Mar 13 2021

Status

approved