A098084 a(n) satisfies P(n) + P(n+1) + a(n) = least prime >= P(n) + P(n+1), where P(i)=i-th prime.

0, 3, 1, 1, 5, 1, 1, 1, 1, 1, 3, 1, 5, 7, 1, 1, 7, 3, 1, 5, 5, 1, 1, 5, 1, 7, 1, 7, 1, 1, 5, 1, 1, 5, 7, 3, 11, 1, 7, 1, 7, 1, 5, 7, 1, 9, 5, 7, 1, 1, 7, 7, 7, 1, 1, 9, 1, 9, 5, 5, 1, 1, 1, 7, 1, 5, 5, 7, 5, 7, 7, 1, 3, 5, 7, 1, 1, 11, 1, 1, 13, 1, 13, 5, 1, 15, 1, 1, 5, 7, 1, 1, 5, 1, 7, 1, 1, 5, 5, 3, 5, 3, 19

Offset: 1

Author

Pierre CAMI, Sep 13 2004

Keywords

• easy
• nonn

Comments

a(n) = 1 iff prime(n) is in A177017. - Robert Israel, Feb 04 2020

Examples

			P(1) + P(2) = 2 + 3 = 5; least prime >= 5 = 5, so a(1)=0.
P(2) + P(3) = 3 + 5 = 8; least prime > 8 = 11, so a(2) = 11 - 8 = 3.
P(3) + P(4) = 5 + 7 = 12; least prime > 12 = 13, so a(3) = 13 - 12 = 1.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

The primes are in A098085.

Cf. A177017.

Programs

Maple

P:= [seq(ithprime(i),i=1..200)]:
map(t -> nextprime(t-1)-t,P[1..-2]+P[2..-1]); # Robert Israel, Feb 04 2020

Mathematica

f[n_] := Block[{k = 0, p = Prime[n] + Prime[n + 1]}, While[ !PrimeQ[p + k], k++ ]; k]; Table[ f[n], {n, 103}] (* Robert G. Wilson v, Sep 24 2004 *)

Extensions

More terms from Robert G. Wilson v, Sep 25 2004