A239864 Starting from any prime p_i (with i = 1, 2, 3 …) sequence lists the minimum number of consecutive primes that must be added to 1 to reach another prime.

1, 16, 2, 2, 4, 2, 2, 2, 2, 2, 8, 2, 8, 6, 2, 2, 12, 16, 2, 4, 6, 2, 2, 6, 2, 4, 2, 4, 2, 2, 14, 2, 2, 8, 8, 6, 4, 2, 4, 2, 12, 2, 10, 22, 2, 10, 16, 8, 2, 2, 40, 8, 4, 2, 2, 12, 2, 18, 6, 6, 2, 2, 2, 8, 2, 18, 30, 6, 4, 4, 4, 2, 20, 10, 4, 2, 2, 4, 2, 2, 20

Offset

1,2

Comments

61 is the minimum prime that can be reached in two ways: adding 1 plus 4 consecutive primes starting from 11 or 2 starting from 29.

Other primes reachable in two ways: 331, 373, 457, 1013, 1321, 1429, 1549, 1901, 2113, 2281, etc.

991 is the minimum prime that can be reached in three ways: adding 1 plus 12 consecutive primes starting from 59, 6 starting from 151 or 2 starting from 491.

Other primes reachable in three ways: 8011, 14827, 24181, 33049, 34351, 40819, 41887, 49549, 59069, 60961, etc.

Links

Paolo P. Lava, Table of n, a(n) for n = 1..1000

Example

a(1) = 1 because p_1 = 2 and 2 + 1 = 3 is prime.
a(2) = 16 because p_2 = 3 and we need to add other 15 consecutive primes plus 1 to reach another prime: 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 1 = 439.
a(3) = 2 because p_3 = 5 and 5 + 7 + 1 = 13 is prime. Etc.

Maple

P:=proc(q) local a, b, c, d, n;
for n from 1 to q do a:=1; b:=ithprime(n); c:=b; d:=b+1;
while not isprime(d) do a:=a+1; c:=nextprime(c); d:=d+c; od;
print(a); od; end: P(10^4);

Mathematica

a[n_] := Module[{s = 1, k = 0, p = Prime[n]}, While[!PrimeQ[s], s += p; p = NextPrime[p]; k++]; k]; Array[a, 100]  (* Amiram Eldar, Mar 31 2019 *)

Crossrefs

Cf. A000040, A239865, A239866, A239867.

Sequence in context: A040250 A065645 A037925 * A040252 A040253 A180730

Adjacent sequences: A239861 A239862 A239863 * A239865 A239866 A239867

Keyword

nonn

Author

Paolo P. Lava, Mar 28 2014

Status

approved