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

1,1

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.

Links

Table of n, a(n) for n=1..15.

Example

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.

Sequence in context: A109736 A119628 A021093 * A011026 A374531 A069805

Adjacent sequences: A342441 A342442 A342443 * A342445 A342446 A342447

Keyword

nonn,more

Author

Bernard Schott, Mar 12 2021

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

Status

approved