A087128 a(1)=1 and, for n>1, a(n) is the smallest positive integer such that 1+Sum_{k=a(n-1)+1..a(n)} k 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

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=a(n-1)+1..t} k == 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

Cf. A087129 (first differences).

Sequence in context: A027010 A038191 A321472 * A154365 A247959 A243799

Adjacent sequences: A087125 A087126 A087127 * A087129 A087130 A087131

Keyword

nonn,changed

Author

John W. Layman, Aug 16 2003

Status

approved