

A087128


a(1)=1 and, for n>1, a(n) is the smallest positive integer such that 1+Sum[k, k=a(n1)+1,...,a(n)] is prime.


3



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(n1) == 1 (mod 3), 1 + Sum(k,k=a(n1+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[n1]+1 do
if isprime(1+(1+A[n1]+b)*(bA[n1])/2) then A[n]:= b; break fi
od od:
seq(A[n], n=1..100); # Robert Israel, Feb 19 2017


CROSSREFS

Sequence in context: A181314 A027010 A038191 * A154365 A247959 A243799
Adjacent sequences: A087125 A087126 A087127 * A087129 A087130 A087131


KEYWORD

nonn


AUTHOR

John W. Layman, Aug 16 2003


STATUS

approved



