A295973 Primes introducing new second differences in A036263.

3, 5, 7, 11, 29, 31, 113, 127, 139, 149, 509, 523, 541, 907, 1069, 1087, 1151, 1327, 1361, 1543, 1669, 1933, 1951, 2971, 2999, 3163, 5381, 5749, 6421, 7963, 9551, 10007, 14143, 15683, 15727, 15823, 16183, 19373, 19609, 20809, 25471, 28277, 28351, 31397, 31469, 31957, 34061, 34123, 35671

Offset: 1

Author

Edward Bernstein, Nov 30 2017

Keywords

• nonn

Comments

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.

Examples

			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, ...
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..324 (first 97 terms from Edward Bernstein)

Crossrefs

Cf. A036263, A295746.

Programs

Maple

A036263s := proc(maxn)
    s := {} ;
    for n from 1 to maxn do
        s := s union {A036263(n)} ;
    end do:
    s ;
end proc:
A295973a := proc(n)
    if n = 1 then
        return 2;
    end if;
    p := nextprime(procname(n-1)) ;
    pidx := numtheory[pi](p) ;
    while true do
        candD := A036263(pidx) ;
        if not candD in A036263s(pidx-1) then
            return ithprime(pidx) ;
        end if ;
        pidx := pidx+1 ;
    end do:
end proc:
A295973 := proc(n)
    nextprime(A295973a(n)) ;
end proc:
seq(A295973(n),n=1..40) ; # R. J. Mathar, Jan 06 2018