A239866 Starting from any prime p_i (with i = 1, 2, 3 …) sequence lists the minimum number of consecutive primes that must be added minus 1 to reach another prime.

17, 1, 2, 2, 2, 2, 8, 2, 40, 2, 2, 4, 2, 2, 8, 4, 4, 2, 2, 6, 2, 4, 38, 4, 2, 4, 4, 10, 4, 2, 2, 6, 12, 8, 4, 2, 4, 38, 10, 8, 2, 4, 2, 2, 4, 2, 2, 2, 12, 2, 6, 2, 2, 4, 20, 8, 4, 2, 2, 2, 4, 2, 2, 8, 4, 2, 12, 2, 8, 2, 4, 16, 2, 2, 2, 22, 8, 2, 2, 2, 2, 4, 2

Offset

1,1

Comments

257 is the minimum prime that can be reached in two ways: adding 4 consecutive primes starting from 59 or 2 starting from 127 and deleting 1.

Other primes reachable in two ways: 389, 479, 491, 761, 863, 1319, 1847, 2131, 3037, 3299, etc.

239 is the minimum prime that can be reached in three ways: adding 8 consecutive primes starting from 17, 4 starting from 53 or 2 starting from 113 and deleting 1.

Other primes reachable in three ways: 24083, 32369, 34259, 40709, 49547, 51997, 60527, 66883, 69959, 75767, etc.

Links

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

Example

a(1) = 17 because p_1 = 2 and we need to add other 16 consecutive primes minus 1 to reach another prime: 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 - 1 = 439.
a(2) = 1 because p_2 = 3 and 3 - 1 = 2 is prime.
a(3) = 2 because p_3 = 5 and 5 + 7 - 1 = 11 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, A239864, A239865, A239867.

Sequence in context: A056110 A040296 A040297 * A040295 A040298 A040300

Adjacent sequences: A239863 A239864 A239865 * A239867 A239868 A239869

Keyword

nonn

Author

Paolo P. Lava, Mar 28 2014

Status

approved