A342440
The longest length of consecutive primes which sums to prime = A342439(n) < 10^n.
Original entry on oeis.org
2, 6, 21, 65, 183, 543, 1587, 4685, 13935, 41708, 125479, 379317, 1150971, 3503790, 10695879, 32729271, 100361001, 308313167, 948694965
Offset: 1
A342439(1) = 5 = 2+3, hence a(1) = 2 since there are 2 terms in this longest sum.
A342439(2) = 41 = 2 + 3 + 5 + 7 + 11 + 13 hence a(2) = 6 since there are 6 terms in this longest sum.
A342453
When A342439(n) is the largest prime < 10^n obtained with the longest sum of the A342440(n) consecutive primes, then a(n) is the first prime of these A342440(n) consecutive primes.
Original entry on oeis.org
2, 2, 7, 3, 3, 7, 7, 7, 11, 2, 19, 5, 5, 2, 13, 5, 5, 7, 11
Offset: 1
A342439(2) = 41 = 2 + 3 + 5 + 7 + 11 + 13 hence a(2) = 2.
A342443
a(n) is the largest prime < 10^n that is the sum of at least two consecutive primes.
Original entry on oeis.org
5, 97, 991, 9949, 99971, 999983, 9999991, 99999989, 999999937, 9999999943, 99999999977, 999999999989, 9999999999763, 99999999999959, 999999999999989
Offset: 1
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.
A342444
a(n) is the smallest number of consecutive primes that are necessary to add to obtain the largest prime = A342443(n) < 10^n.
Original entry on oeis.org
2, 3, 5, 9, 5, 29, 281, 1575, 599, 7, 17, 3, 6449, 2725361, 163315
Offset: 1
A342443(1) = 5 = 2 + 3, hence a(1) = 2.
A342443(2) = 97 = 29 + 31 + 37, hence a(2) = 3.
From _Jon E. Schoenfield_, Mar 14 2021: (Start)
a(n) =
sum of consecutive primes number of
----------------------------------------- consecutive
n A342454(n) + ... = A342443(n) primes
-- ----------------------------------------- -----------
1 2 + 3 = 5 2
2 29 + 31 + 37 = 97 3
3 191 + ... = 991 5
4 1087 + ... = 9949 9
5 19979 + ... = 99971 5
6 34337 + ... = 999983 29
7 34129 + ... = 9999991 281
8 54829 + ... = 99999989 1575
9 1665437 + ... = 999999937 599
10 1428571363 + ... = 9999999943 7
11 5882352691 + ... = 99999999977 17
12 333333333299 + ... = 999999999989 3
13 1550560001 + ... = 9999999999763 6449
14 13384757 + ... = 99999999999959 2725361
(End)
A342454
a(n) = first prime of the A342444(n) consecutive primes summing to A342443(n).
Original entry on oeis.org
2, 29, 191, 1087, 19979, 34337, 34129, 54829, 1665437, 1428571363, 5882352691, 333333333299, 1550560001, 13384757, 6121296037
Offset: 1
A342439(1) = 2 + 3 = 5 hence a(1) = 2.
A342439(2) = 29 + 31 + 37 = 97 hence a(2) = 29.
Showing 1-5 of 5 results.
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