

A073883


a(1)=1. For n > 1, a(n) = the smallest positive integer not included earlier such that the nth partial sum is n times a prime.


3



1, 3, 2, 6, 13, 5, 19, 7, 43, 11, 33, 61, 17, 45, 79, 23, 125, 29, 67, 31, 157, 37, 129, 41, 91, 147, 47, 215, 53, 233, 59, 123, 259, 203, 71, 143, 73, 301, 235, 83, 329, 89, 433, 97, 277, 101, 195, 103, 299, 107, 209, 109, 321, 113, 883, 127, 355, 131, 485, 137
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OFFSET

1,2


COMMENTS

Equivalently, for n > 1, a(n) is the smallest number not already in the sequence such that the arithmetic mean of the first n terms is prime.  Derek Orr, Jun 26 2015
Conjectured not to be a permutation of the natural numbers. The numbers that have not been used before the 2000th term: 4, 8, 9, 10, 12, 14, 15, 16, 18, 20, 22, ...  Derek Orr, Jun 26 2015


LINKS

Derek Orr, Table of n, a(n) for n = 1..2000


PROG

(PARI) v=[1]; n=1; while(#v<200, s=(n+vecsum(v))/(#v+1); if(type(s)=="t_INT", if(isprime(s)&&!vecsearch(vecsort(v), n), v=concat(v, n); n=0)); n++); v \\ Derek Orr, Jun 26 2015


CROSSREFS

Sequence in context: A052616 A091461 A078091 * A248982 A289069 A074718
Adjacent sequences: A073880 A073881 A073882 * A073884 A073885 A073886


KEYWORD

nonn


AUTHOR

Amarnath Murthy, Aug 16 2002


EXTENSIONS

Corrected and extended by Sascha Kurz, Feb 01 2003


STATUS

approved



