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a(n) is the smallest number of consecutive primes that are necessary to add to obtain the largest prime = A342443(n) < 10^n.
5

%I #28 Mar 16 2021 09:17:15

%S 2,3,5,9,5,29,281,1575,599,7,17,3,6449,2725361

%N a(n) is the smallest number of consecutive primes that are necessary to add to obtain the largest prime = A342443(n) < 10^n.

%C There are at least two consecutive primes in each sum.

%C The corresponding largest primes obtained are in A342443, and the first primes of these a(n) consecutive primes are in A342454.

%e A342443(1) = 5 = 2 + 3, hence a(1) = 2.

%e A342443(2) = 97 = 29 + 31 + 37, hence a(2) = 3.

%e From _Jon E. Schoenfield_, Mar 14 2021: (Start)

%e a(n) =

%e sum of consecutive primes number of

%e ----------------------------------------- consecutive

%e n A342454(n) + ... = A342443(n) primes

%e -- ----------------------------------------- -----------

%e 1 2 + 3 = 5 2

%e 2 29 + 31 + 37 = 97 3

%e 3 191 + ... = 991 5

%e 4 1087 + ... = 9949 9

%e 5 19979 + ... = 99971 5

%e 6 34337 + ... = 999983 29

%e 7 34129 + ... = 9999991 281

%e 8 54829 + ... = 99999989 1575

%e 9 1665437 + ... = 999999937 599

%e 10 1428571363 + ... = 9999999943 7

%e 11 5882352691 + ... = 99999999977 17

%e 12 333333333299 + ... = 999999999989 3

%e 13 1550560001 + ... = 9999999999763 6449

%e 14 13384757 + ... = 99999999999959 2725361

%e (End)

%Y Cf. A067377, A342439, A342440, A342443, A342453, A342454.

%K nonn,more

%O 1,1

%A _Bernard Schott_, Mar 12 2021

%E a(6)-a(9) from _Jinyuan Wang_, Mar 13 2021

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

%E a(11)-a(14) from _Jon E. Schoenfield_, Mar 14 2021