OFFSET
2,1
COMMENTS
a(n)=1 iff p_n is second of twin primes (A006512); for n > 4, a(n)=2 iff p_n is second of cousin primes (A046132). It is interesting to continue this sequence in order to find big jumps such as a(31)-a(30). Is it true that such jumps can be arbitrarily large, either (a) in the sense of differences a(n+1)-a(n), or (b) in the sense of ratios a(n+1)/a(n)?
Conjecture. For every odd prime p, the sequence {|2^n - p|} contains at least one prime. The record values of the sequence appear at n = 2, 10, 31, 68, 341, ... and are 3, 4, 47, 791, ... Note that up to now the value a(341) is not known. Charles R Greathouse IV calculated the following two values: a(815)=16464, a(591)=58091 and noted that a(341) is much larger [private communication, May 27 2010]. - Vladimir Shevelev, May 29 2010
LINKS
Amiram Eldar, Table of n, a(n) for n = 2..340
MATHEMATICA
lm[n_]:=Module[{m=1}, While[!PrimeQ[Abs[2^m-n]], m++]; m]; Table[lm[i], {i, Prime[ Range[2, 100]]}] (* Harvey P. Dale, Aug 11 2014 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Apr 19 2010, Aug 15 2010
EXTENSIONS
Beginning with a(31), the terms were calculated by Zak Seidov - private communication, Apr 20 2010
Sequence extended by R. J. Mathar via the Seqfan Discussion List, Aug 15 2010
STATUS
approved