A087128 - OEIS

A087128

a(1)=1 and, for n>1, a(n) is the smallest positive integer such that 1+Sum[k, k=a(n-1)+1,...,a(n)] is prime.

1, 2, 5, 6, 13, 22, 25, 34, 37, 46, 58, 61, 73, 97, 106, 142, 145, 178, 181, 193, 202, 205, 217, 226, 238, 253, 277, 286, 298, 313, 346, 358, 382, 385, 394, 430, 433, 442, 466, 502, 529, 541, 553, 562, 565, 586, 682, 685, 694, 697, 709, 718, 721, 733, 838, 841

(list; graph; refs; listen; history; text; internal format)

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