# [seqfan] Extremely unpleasant event

Sun Aug 15 17:10:25 CEST 2010

```Dear SeqFans,

It is happend extremely unpleasant event which could have far very negative corollaries.
19.04.10 I sent into OEIS the following sequence:

%I A176494
%S A176494 3,1,1,2,1,2,1,2,4,1,3,2,1,2,4,4,1,3,2,1,3,2,4,3,2,1,2,1,2,47,2
%N A176494 Least m>=1 for which |2^m-p_n| is prime, where p_n is the nth prime, n>=2
%C A176494 a(n)=1 iff p_n is second of twin primes (A006512); for n>4, a(n)=2 iff p_n is second of cousing primes (A046132). It is interesting to continue this sequence in order to find big jumps as a(31)-a(30). Is it true that such jumps could be arbitrary large (a) in the sense of differences a(n+1)-a(n); (b) in the sense of ratios a(n+1)/a(n)?
%Y A176494 A176303 A175347 A006512 A046132
%K A176494 nonn
%O A176494 2,1
%A A176494 Vladimir Shevelev (shevelev(AT)bgu.ac.il), Apr 19 2010

A176494Least m>=1 for which |2^m-p_n| is prime, where p_n is the nth prime.

6, 1, 8, 1, 3, 5, 2, 4, 4, 1, 6, 1, 2, 1, 5, 5, 2, 1, 2, 4, 1, 8, 4, 6, 8, 1, 3, 2, 1, 4, 7, 2, 1, 9, 791, 4, 1 (list; graph; listen)

OFFSET 2,1
COMMENT 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 arbitrary 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 records of the sequence appear in points 2,10,31,68,341,... and equal to 3, 4, 47, 791,... Note that up to now the value a(341) is not known. Charles Greathouse(charles.greatehouse(AT)case.edu) calculated the following two values: a(815)=16464, a(591)=58091 and noted that a(341)is much larger.-Private communication at 27.05.10. [From Vladimir Shevelev (shevelev(AT)bgu.ac.il), May 29 2010]
CROSSREFS Cf. A176303 A175347 A006512 A046132
Sequence in context: A089762 A030347 A010275 this_sequence A157229 A107297 A107296
Adjacent sequences: A176491 A176492 A176493 this_sequence A176495 A176496 A176497
KEYWORD nonn
AUTHOR Vladimir Shevelev (shevelev(AT)bgu.ac.il), Apr 19 2010
EXTENSIONS Beginning with a(31) the terms were calculated by Zak Seidov (seidov(AT)bgu.ac.il)-private communication at 20.04.10. Vladimir Shevelev (shevelev(AT)bgu.ac.il), May 29 2010

What is this???
Before I received  the following message:
>Vladimir, I just came across sequence A176494 by chance today and I
>must confess that I don't understand the values at all.

>Definition:
>Least m>=1 for which |2^m-p_n| is prime, where p_n is the nth prime.

>a(4) is given as 8, but |2^8 - p_4| = |256 - 7| = 249 = 3 * 83.
>a(2) is given as 6, and |2^6 - p_2| is prime, but so is |2^3 - p_2| = 5.
>In fact most of the terms, as listed, seem wrong.

>But perhaps I am only misinterpreting the sequence?

>I see some similarities between the sequence given and what I
>calculate, though: your a(36) = 791, as does my a(68) which
>corresponds to the prime |2^791 - 337|.

>Charles Greathouse
>Analyst/Programmer
>Case Western Reserve University
If we should verify ALL our sequences??
Regards,