A261271 a(n) = a(n-1)-1+p, where p is the smallest prime number that is not a factor of a(n-1)-1.

1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 37, 41, 43, 47, 49, 53, 55, 59, 61, 67, 71, 73, 77, 79, 83, 85, 89, 91, 97, 101, 103, 107, 109, 113, 115, 119, 121, 127, 131, 133, 137, 139, 143, 145, 149, 151, 157, 161, 163, 167, 169, 173, 175

Offset

1,2

Comments

Alternative definition: a(n) = smallest number > a(n-1) coprime with a(n-1)-1. Therefore, the sequence contains all prime numbers in ascending order.

Except for a(2), all terms are odd.

The sequence comprises the largest terms in A123882 appearing in order.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(14)=37 because a(13)=31, the smallest prime not a factor of 30 is p = 7, and 30+7 = 37.

Maple

f:= proc(k) local p;
  p:= 2;
  while k-1 mod p = 0 do p:= nextprime(p) od;
  k-1+p
end proc:
A[1]:= 1: A[2]:= 2:
for n from 3 to 100 do A[n]:= f(A[n-1]) od:
seq(A[i], i=1..100); # Robert Israel, Oct 23 2018

Prog

(PARI) p(n)=pp=1; while(n%prime(pp)==0, pp++); prime(pp);
first(m)=my(v=vector(m)); v[1]=1; v[2]=2; for(i=3, m, v[i]=v[i-1]-1+p(v[i-1]-1)); v; /* Anders Hellström, Aug 13 2015 */

Crossrefs

Cf. A000040, A123882.

Sequence in context: A038179 A192489 A161578 * A335284 A308966 A186891

Adjacent sequences: A261268 A261269 A261270 * A261272 A261273 A261274

Keyword

nonn,easy

Author

Bob Selcoe, Aug 13 2015

Status

approved