A073602 a(n) is the smallest prime different from a(k) for k < n such that sum(a(j), j=1..n) is a multiple of the n-th prime.

2, 7, 11, 29, 17, 103, 137, 131, 23, 149, 73, 317, 67, 181, 163, 127, 233, 487, 557, 97, 593, 367, 113, 199, 1249, 2143, 47, 617, 263, 877, 19, 1213, 349, 577, 383, 311, 643, 3, 1151, 331, 677, 2521, 397, 1153, 1381, 1601, 277, 157, 631, 433, 179, 373, 443

Offset

1,1

Comments

Conjecture: Every prime belongs to this sequence.

Among first 10^6 terms first missing primes are {5, 13, 41, 61, 71, 89, 173, 193, 227, 229, 239, 283, 313, 337, 389, 401, 439, 449, 461, 467, 479, 499, 509, 541}; only two "fixed points" are a(1) = prime(1) = 2 and a(9) = prime(9) = 23. - Zak Seidov, Jun 12 2015

Also, among first 10^6 terms there are just 16931 "early birds": terms a(k) such that a(k) < A000040(k); first values of k are: 27, 31, 38, 48, 51, 113, 99, 51, 113, 137, 191, 240, 254, 297, 308, ... - Zak Seidov, Jun 12 2015

Links

Zak Seidov, Table of n, a(n) for n = 1..10000

Example

a(5) = 17 since 2 + 7 + 11 + 29 + 17 = 66 is a multiple of 11, the fifth prime. For the smaller primes 3, 5, 13 the corresponding sums 52, 54, 62 are not multiples of 11.

Mathematica

t = {2}; Do[p = Prime[n]; i = 2; While[! Divisible[Total[t] + (y = Prime[i]), p] || MemberQ[t, y], i++]; AppendTo[t, y], {n, 2, 53}]; t (* Jayanta Basu, Jul 02 2013 *)

Prog

(PARI) vsearch(n, v)=local(j, s); j=1; s=matsize(v)[2]; while(j<=s&&n!=v[j], j++); j<=s
{m=54; v=[]; n=1; while(n<=m, p=2; while(vsearch(p, v)||((sum(j=1, matsize(v)[2], v[j])+p)%prime(n))>0, p=nextprime(p+1)); print1(p, ", "); v=concat(v, p); n++)}

Crossrefs

Sequence in context: A309469 A309470 A309471 * A057025 A055469 A361151

Adjacent sequences: A073599 A073600 A073601 * A073603 A073604 A073605

Keyword

nonn

Author

Amarnath Murthy, Aug 04 2002

Extensions

Edited and extended by Klaus Brockhaus, Aug 10 2002

Status

approved