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

1,1

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)

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 *)

Prog

(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

Crossrefs

Cf. A079849.

Sequence in context: A350100 A038905 A019405 * A329749 A237810 A073434

Adjacent sequences: A079845 A079846 A079847 * A079849 A079850 A079851

Keyword

nice,nonn

Author

Amarnath Murthy, Feb 18 2003

Extensions

More terms from Max Alekseyev, Feb 14 2005

Status

approved