# Adding and Subtracting 1 and the First n Primes to Get the Next Prime (Part 2)

In part 1 I dealt with even-indexed primes. In this post I want to show the first few examples of how to obtain the odd-indexed prime numbers using the addition or subtraction of 1 and all the other preceding primes. The odd-indexed primes are covered by the OEIS sequence A031368.

The summation for each prime is done using the rules established by Curiosa 67 from Scripta Mathematica.

### Examples

For convenience, you can see below the original text of Curiosa 67 by Renato Della Torre.

Like in Curiosa 67, the examples below have the terms arranged in increasing order (according to their absolute value). The largest prime in the summation is always multiplied by 2 or -2.

p(1)=2=2*1

p(3) =5=1-2+2*3

p(5)=11=1-2+3-5+2*7

p(7)=17=-1-2+3-5+7-11+2*13

p(9)=23=−1+2−3−5+7−11+13−17+2*19

p(11)=31=−1+2−3+5−7−11+13+17−19−23+2*29

p(13)=41=1+2−3−5-7−11+13−17+19−23+29-31+2*37

p(15)=47=−1+2−3−5−7−11+13−17+19−23+29−31+37−41+2*43

p(17)=59=-1-2−3−5−7−11+13−17+19−23+29−31+37−41+43−47+2*53