A257077 a(n) = prime(n)-prime(1)-prime(2)-...-prime(k), while the result > 0.

2, 1, 3, 2, 1, 3, 7, 2, 6, 1, 3, 9, 13, 2, 6, 12, 1, 3, 9, 13, 15, 2, 6, 12, 20, 1, 3, 7, 9, 13, 27, 2, 8, 10, 20, 22, 28, 3, 7, 13, 19, 21, 31, 33, 37, 2, 14, 26, 30, 32, 36, 1, 3, 13, 19, 25, 31, 33, 39, 43, 2, 12, 26, 30, 32, 36, 3, 9, 19, 21, 25, 31, 39

Offset: 1

Author

Carlos Eduardo Olivieri, Apr 15 2015

Keywords

• nonn
• easy

Comments

It appears that a(n) = n occurs only for n=3, 7, 13. It also appears that a(n+1) is never equal to a(n).

The list of indices such that a(n)=1 correspond to the primes in A053845. - Michel Marcus, Apr 16 2015

In other words, a(n) = prime(n) - A007504(k) for largest k such that prime(n) > A007504(k). - Danny Rorabaugh, Apr 20 2015

Examples

			a(1) = 2, since there is no previous prime.
a(2) = 1, since 3 - 2 = 1.
a(3) = 3, since 5 - 2 = 3.
a(4) = 2, since 7 - 2 - 3 = 2.
a(5) = 1, since 11 - 2 - 3 - 5 = 1.
a(6) = 3, since 13 - 2 - 3 - 5 = 3.
a(13) = 13, since 41 - 2 - 3 - 5 - 7 - 11 = 13.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007504, A013918.

Programs

Mathematica

lst = {}; i = 1; While[i <= 1000, x = Prime[i]; k = 1; While[x > 0, x -= Prime[k]; k++]; x += Prime[k - 1]; AppendTo[lst, x]; i++]; lst

PARI

a(n) = {s = prime(n); k = 1; while ((ns = (s - prime(k))) > 0, s = ns; k++); s;} \\ Michel Marcus, Apr 16 2015

PARI

s=0; q=2; forprime(p=2,10, if(s+q>p, s+=q; q=nextprime(q+1)); print1(p-s", ")) \\ Charles R Greathouse IV, Apr 22 2015

Formula

a(n) << sqrt(n)*log(n). - Charles R Greathouse IV, Apr 23 2015