A342444 a(n) is the smallest number of consecutive primes that are necessary to add to obtain the largest prime = A342443(n) < 10^n.

2, 3, 5, 9, 5, 29, 281, 1575, 599, 7, 17, 3, 6449, 2725361, 163315

Offset: 1

Author

Bernard Schott, Mar 12 2021

Keywords

• nonn
• more

Comments

There are at least two consecutive primes in each sum.

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

Examples

			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)
		

Crossrefs

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

Extensions

a(6)-a(9) from Jinyuan Wang, Mar 13 2021

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

a(11)-a(14) from Jon E. Schoenfield, Mar 14 2021

a(15) from Max Alekseyev, Dec 11 2024