

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
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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(ps", ")) \\ 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



