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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
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A038179 A192489 A161578 * A335284 A308966 A186891
KEYWORD
nonn,easy
AUTHOR
Bob Selcoe, Aug 13 2015
STATUS
approved

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Last modified March 28 16:58 EDT 2024. Contains 371254 sequences. (Running on oeis4.)