A079848 Smallest primes such that a(j) - a(k) are all different.

2, 3, 5, 11, 23, 37, 47, 97, 101, 149, 211, 233, 353, 383, 487, 641, 757, 797, 919, 1097, 1163, 1381, 1409, 1481, 1777, 1997, 2287, 2417, 2969, 3049, 3371, 3529, 3929, 4231, 4759, 5279, 5449, 5717, 5953, 6529, 6983, 7583, 8053, 8819, 9043, 10133, 10799

Offset: 1

Author

Amarnath Murthy, Feb 18 2003

Keywords

• nice
• nonn

Comments

This is the slowest-growing prime B2 sequence. See A005282. - T. D. Noe, Mar 24 2007

Links

• T. D. Noe, Table of n, a(n) for n=1..4084 (terms less than 2*10^9)

Crossrefs

Cf. A079849.

Programs

Mathematica

terms = 100; a = Table[0, {terms}]; s={}; k=0; A079848list = Reap[For[p=2, p < 10^5, p = NextPrime[p], j=1; While[j <= k && FreeQ[s, p-a[[j]]], j++]; If[j>k, For[j=1, j <= k, j++, s = Union[s, {p-a[[j]]}]]; k++; a[[k]] = p; Print[p]; Sow[p]; If[k == terms, Break[]]]]][[2, 1]]; (* Jean-François Alcover, Nov 02 2016, adapted from Max Alekseyev's PARI code *)

PARI

a=vector(100);s=Set();k=0;forprime(p=2,10^5,j=1;while(j<=k&&!setsearch(s,p-a[j]),j++);if(j>k, for(j=1,k,s=setunion(s,[p-a[j]]));k++;a[k]=p;print1(" ",p);if(k==100,break))) \\ Max Alekseyev, Feb 14 2005

Python

from itertools import count, islice
from sympy import nextprime
def A079848_gen(): # generator of terms
    aset2, alist, k = set(), [], 0
    while (k:=nextprime(k)):
        bset2 = set()
        for a in alist:
            if (b:=k-a) in aset2:
                break
            bset2.add(b)
        else:
            yield k
            alist.append(k)
            aset2.update(bset2)
A079848_list = list(islice(A079848_gen(),30)) # Chai Wah Wu, Sep 11 2023

Extensions

More terms from Max Alekseyev, Feb 14 2005