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A257077 a(n) = prime(n)-prime(1)-prime(2)-...-prime(k), while the result > 0. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

LINKS

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

FORMULA

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

EXAMPLE

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.

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

PROG

(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

CROSSREFS

Cf. A007504, A013918.

Sequence in context: A329508 A329515 A169742 * A086414 A098896 A108371

Adjacent sequences:  A257074 A257075 A257076 * A257078 A257079 A257080

KEYWORD

nonn,easy

AUTHOR

Carlos Eduardo Olivieri, Apr 15 2015

STATUS

approved

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Last modified February 28 14:16 EST 2021. Contains 341707 sequences. (Running on oeis4.)