OFFSET
1,2
COMMENTS
It appears that, for n>4, all differences a(n+1)-a(n) are multiples of 3. The sequence of differences is A087129.
This is true because if a(n-1) == 1 (mod 3), 1 + Sum(k,k=a(n-1+1..t) == 2 (t^2+t) mod 3, so this would be divisible by 3 unless t == 1 (mod 3). - Robert Israel, Feb 19 2017
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
a(2)=2 since 1+(2)=3 is prime. a(3)=5 since 1+(3+4+5)=13 is prime.
MAPLE
A[1]:= 1:
for n from 2 to 100 do
for b from A[n-1]+1 do
if isprime(1+(1+A[n-1]+b)*(b-A[n-1])/2) then A[n]:= b; break fi
od od:
seq(A[n], n=1..100); # Robert Israel, Feb 19 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
John W. Layman, Aug 16 2003
STATUS
approved