

A350118


Primes p for which the smallest m such that p*2^m + 1 is prime increases. Sequence terminates with the smallest prime Sierpiński number.


1



2, 3, 7, 17, 19, 31, 47, 383, 2897, 3061, 5297, 7013, 10223
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OFFSET

1,1


COMMENTS

The smallest prime Sierpiński number is likely to be 271129.
Related to A058887: this sequence is A058887 with repeated values removed. The following list shows that relation between these two sequences:
...
a(N) is the smallest prime Sierpiński number, A350119(N) = 1 => A058887(k) = a(N) for all k >= A350119(N1).


LINKS



EXAMPLE

Let b(p) be the smallest m such that p*2^m + 1 is prime. We have a(1) = 2 with b(2) = 0.
The least prime p such that b(p) > 0 is p = 3 with b(3) = 1, so a(2) = 3.
The least prime p such that b(p) > 1 is p = 7 with b(7) = 2, so a(3) = 7.
The least prime p such that b(p) > 2 is p = 17 with b(17) = 3, so a(4) = 17.
The least prime p such that b(p) > 3 is p = 19 with b(19) = 6, so a(5) = 19.
The least prime p such that b(p) > 6 is p = 31 with b(31) = 8, so a(6) = 31.
The least prime p such that b(p) > 8 is p = 47 with b(47) = 583, so a(7) = 47.


PROG

(PARI) b(p) = for(k=0, oo, if(isprime(p*2^k+1), return(k)))
list(lim) = if(lim>=2, my(v=[2], r=0); forprime(p=2, lim, if(b(p)>r, r=b(p); v=concat(v, p))); v)


CROSSREFS



KEYWORD

nonn,fini,hard,more


AUTHOR



STATUS

approved



