A295973 - OEIS

%I #45 Mar 02 2019 04:22:22

%S 3,5,7,11,29,31,113,127,139,149,509,523,541,907,1069,1087,1151,1327,

%T 1361,1543,1669,1933,1951,2971,2999,3163,5381,5749,6421,7963,9551,

%U 10007,14143,15683,15727,15823,16183,19373,19609,20809,25471,28277,28351,31397,31469,31957,34061,34123,35671

%N Primes introducing new second differences in A036263.

%C This list consists of those primes corresponding to new second differences in A036263. There are 97 new second differences introduced up to the 100000th prime.

%H Robert G. Wilson v, <a href="/A295973/b295973.txt">Table of n, a(n) for n = 1..324</a> (first 97 terms from Edward Bernstein)

%e The new values in A036263 are 1, 0, 2, -2, -4, 4, 10, -10, 8, -8, ... at indices 1, 2, 3, 4, 9, 10, 29, 30, ... and the middle primes of the prime triple starting at these indices are 3, 5, 7, 11, 29, ...

%p A036263s := proc(maxn)

%p     s := {} ;

%p     for n from 1 to maxn do

%p         s := s union {A036263(n)} ;

%p     end do:

%p     s ;

%p end proc:

%p A295973a := proc(n)

%p     if n = 1 then

%p         return 2;

%p     end if;

%p     p := nextprime(procname(n-1)) ;

%p     pidx := numtheory[pi](p) ;

%p     while true do

%p         candD := A036263(pidx) ;

%p         if not candD in A036263s(pidx-1) then

%p             return ithprime(pidx) ;

%p         end if ;

%p         pidx := pidx+1 ;

%p     end do:

%p end proc:

%p A295973 := proc(n)

%p     nextprime(A295973a(n)) ;

%p end proc:

%p seq(A295973(n),n=1..40) ; # _R. J. Mathar_, Jan 06 2018

%Y Cf. A036263, A295746.

%K nonn

%O 1,1

%A _Edward Bernstein_, Nov 30 2017