cp's OEIS Frontend

A295973 Primes introducing new second differences in A036263.

%I A295973 #45 Mar 02 2019 04:22:22
%S A295973 3,5,7,11,29,31,113,127,139,149,509,523,541,907,1069,1087,1151,1327,
%T A295973 1361,1543,1669,1933,1951,2971,2999,3163,5381,5749,6421,7963,9551,
%U A295973 10007,14143,15683,15727,15823,16183,19373,19609,20809,25471,28277,28351,31397,31469,31957,34061,34123,35671
%N A295973 Primes introducing new second differences in A036263.
%C A295973 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 A295973 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 A295973 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 A295973 A036263s := proc(maxn)
%p A295973     s := {} ;
%p A295973     for n from 1 to maxn do
%p A295973         s := s union {A036263(n)} ;
%p A295973     end do:
%p A295973     s ;
%p A295973 end proc:
%p A295973 A295973a := proc(n)
%p A295973     if n = 1 then
%p A295973         return 2;
%p A295973     end if;
%p A295973     p := nextprime(procname(n-1)) ;
%p A295973     pidx := numtheory[pi](p) ;
%p A295973     while true do
%p A295973         candD := A036263(pidx) ;
%p A295973         if not candD in A036263s(pidx-1) then
%p A295973             return ithprime(pidx) ;
%p A295973         end if ;
%p A295973         pidx := pidx+1 ;
%p A295973     end do:
%p A295973 end proc:
%p A295973 A295973 := proc(n)
%p A295973     nextprime(A295973a(n)) ;
%p A295973 end proc:
%p A295973 seq(A295973(n),n=1..40) ; # _R. J. Mathar_, Jan 06 2018
%Y A295973 Cf. A036263, A295746.
%K A295973 nonn
%O A295973 1,1
%A A295973 _Edward Bernstein_, Nov 30 2017