A125148 a(n) = smallest prime p = z + x, where x is the n-th odd composite number not divisible by 5 and z is a multiple of 10.

19, 31, 37, 43, 59, 59, 61, 67, 73, 79, 97, 101, 97, 101, 103, 109, 131, 127, 139, 131, 163, 139, 163, 151, 163, 157, 163, 179, 181, 179, 181, 197, 193, 197, 199, 211, 223, 227, 229, 223, 227, 229, 241, 241, 257, 263, 257, 269, 263, 269, 271, 277, 283, 349

Offset

1,1

Comments

Conjecture: for every odd (prime or nonprime) number x>=1 that is not a multiple of 5 there exists a prime p such that p = z + x; where z is a multiple of 10.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

The first and second odd composite number not divisible by 5 are 9 and 21, thus 19 = 10 + 9 and 31 = 10 + 21 are the first and second term of the sequence.

Mathematica

Module[{nn=300, oddcomps, z}, oddcomps=Select[Range[3, nn, 2], !PrimeQ[#] && !Divisible[#, 5]&]; Table[z=10; While[!PrimeQ[z+oddcomps[[n]]], z=z+10]; z+oddcomps[[n]], {n, Length[oddcomps]}]] (* Harvey P. Dale, Oct 01 2013 *)

Prog

(PARI) {m=280; for(x=2, m, if(x%2!=0&&x%5!=0&&!isprime(x), z=10; while(z<10^5&&!isprime(a=z+x), z+=10); print1(if(z<10^5, a, 0), ", ")))} - Klaus Brockhaus, Jan 24 2007

Crossrefs

Sequence in context: A330275 A038672 A250216 * A214798 A040066 A339465

Adjacent sequences: A125145 A125146 A125147 * A125149 A125150 A125151

Keyword

nonn

Author

Tomas Xordan, Jan 11 2007

Extensions

Edited by Klaus Brockhaus, Jan 24 2007

Status

approved