OFFSET
1,2
COMMENTS
Is this sequence finite?
For n>1, a(n)-2 is prime or semiprime.
If a(n) is the lesser of a twin prime pair, then a(n+1) = a(n)+2 (= a(1)*a(n)+2). - M. F. Hasler, Feb 11 2012
There are exactly 3478486 terms < 10^18 with a(3478486) = 999999462621744733. - Terentyev Oleg, Mar 09 2012
LINKS
M. F. Hasler, Table of n, a(n) for n = 1..20000
Discussion at forum dxdy.ru (in Russian)
EXAMPLE
a(2) = a(1)^2+2, a(3) = a(1)*a(2)+2, a(4) = a(1)*a(3)+2, a(5) = a(2)^2+2, a(6)=a(1)*a(5)+2, a(7) = a(1)*a(5)+2, a(8) = a(2)*a(3)+2, ...
a(16027) = 14228123711 is the lesser of a twin prime pair, it is followed by the greater twin prime, a(16028) = 14228123713.
MATHEMATICA
a = {1}; s = {}; While[s = Union[s, Select[a*a[[-1]] + 2, PrimeQ]]; s != {} && Length[a] < 100, AppendTo[a, s[[1]]]; s = Rest[s]]; a (* T. D. Noe, Mar 12 2012 *)
PROG
(PARI) a=Set(p=1); for(n=1, 999, until(bigomega(p-2)<3 & !setminus(Set(factor(p-2)[, 1]~), a), p=nextprime(p+2)); a=setunion(a, Set(p))); vecsort(eval(a)) \\ M. F. Hasler, Feb 10 2012
(PARI) {a=[r=1]; for(n=1, 9999, while(a[r]^2+2<=a[n], r++); m=0; s=r; for(i=r, n, while(s>1&&a[s-1]*a[i]+2>a[n], s--); for( j=s, i, m & a[j]*a[i]+2>m & break; isprime(a[j]*a[i]+2) & m=a[j]*a[i]+2 )); a=concat(a, m))} \\ M. F. Hasler, Feb 10 2012
CROSSREFS
KEYWORD
nonn
AUTHOR
Max Alekseyev, Jan 16 2012
STATUS
approved