A342439
Let S(n,k) denote the set of primes < 10^n which are the sum of k consecutive primes, and let K = maximum k >= 2 such that S(n,k) is nonempty; then a(n) = max S(n,K).
Original entry on oeis.org
5, 41, 953, 9521, 92951, 997651, 9964597, 99819619, 999715711, 9999419621, 99987684473, 999973156643, 9999946325147, 99999863884699, 999999149973119, 9999994503821977, 99999999469565483, 999999988375776737, 9999999776402081701
Offset: 1
a(1) = 5 = 2+3.
a(2) = 41 = 2 + 3 + 5 + 7 + 11 + 13; note that 97 = 29 + 31 + 37 is prime, sum of 3 consecutive primes, but 41 is obtained by adding 6 consecutive primes, so, 97 is not a term.
A342440(7) = 1587, and there exist two 7-digit primes that are sum of 1587 consecutive primes; as 9951191 = 5+...+13399 < 9964597 = 7+...+13411 hence a(7) = 9964597.
A342440(15) = 10695879 , and there exist two 15-digit primes that are sum of 10695879 consecutive primes; as 999998764608469 = 7+...+192682309 < 999999149973119 = 13+...+192682337, hence a(15) = 999999149973119.
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 1-4 of 4 results.
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