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

1,1

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.

Links

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

Example

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, ...

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

Crossrefs

Cf. A036263, A295746.

Sequence in context: A344411 A265687 A023368 * A142247 A167895 A106712

Adjacent sequences: A295970 A295971 A295972 * A295974 A295975 A295976

Keyword

nonn

Author

Edward Bernstein, Nov 30 2017

Status

approved