A175443 a(1)=2, a(n+1) = smallest prime > a(n) such that a(n+1)+a(n) is multiple of 5.

2, 3, 7, 13, 17, 23, 37, 43, 47, 53, 67, 73, 97, 103, 107, 113, 127, 163, 167, 173, 197, 223, 227, 233, 257, 263, 277, 283, 307, 313, 317, 353, 367, 373, 397, 433, 457, 463, 467, 503, 547, 563, 577, 593, 607, 613, 617, 643, 647, 653, 677, 683, 727, 733, 757

Offset: 1

Author

Zak Seidov, May 28 2010

Keywords

• nonn
• easy

Comments

Lexicographically first subsequence of primes such that the sum of any two adjacent terms is a multiple of 5. - Charles R Greathouse IV, Apr 13 2015

For n >= 1, a(2*n) == 3 (mod 10) and a(2*n+1) == 7 (mod 10). - Robert Israel, Apr 13 2015

Links

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

Crossrefs

Cf. A175451.

Programs

Maple

a[1]:= 2: a[2]:= 3:
for n from 2 to 99 do
for t from a[n]+ (-2*a[n] mod 10) by 10 while not isprime(t) do od:
a[n+1]:= t;
od:
seq(a[n],n=1..100); # Robert Israel, Apr 13 2015

Mathematica

spm5[n_]:=Module[{p=NextPrime[n]},While[!Divisible[n+p,5],p = NextPrime[ p]]; p]; NestList[spm5,2,60] (* Harvey P. Dale, Jan 02 2017 *)

PARI

list(lim)=my(v=List([2])); forprime(p=2,lim,if((v[#v]+p)%5,, listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Apr 13 2015