OFFSET
2,1
COMMENTS
The limit of a(n) as n goes to infinity is infinity.
Conjecture: every a(n), except for a(7) = 191, is the lesser of a pair of cousin primes p and p+4, (see A023200).
MATHEMATICA
myPrime=Select[Table[Prime[n], {n, 3000000}], Mod[#, 4]==3&];
binarySearch[lst_, find_]:=Module[{lo=1, up=Length[lst], v}, (While[lo<=up, v=Floor[(lo+up)/2]; If[lst[[v]]-find==0, Return[v]]; If[lst[[v]]<find, lo=v+1, up=v-1]]; 0)];
myPrimeQ[n_]:=binarySearch[myPrime, n];
nextMyPrime[n_, offset_Integer:1]:=myPrime[[myPrimeQ[NextPrime[n, NestWhile[#1+1&, 1, !myPrimeQ[NextPrime[n, #1]]>0&]]]+offset-1]];
z=1; (*contains exactly ONE myPrime in the interval*)
Table[myPrime[[NestWhile[#1+1&, 1, !((nextMyPrime[n myPrime[[#1]], z+1]>n myPrime[[#1+1]]))&]]], {n, 2, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Shevelev and Peter J. C. Moses, Jan 23 2013
STATUS
approved