

A356188


a(1)=1; for n > 1, if a(n1) is prime then a(n) = the smallest number not yet in the sequence. Otherwise a(n) = a(n1) + n  1.


1



1, 2, 3, 4, 8, 13, 5, 6, 14, 23, 7, 9, 21, 34, 48, 63, 79, 10, 28, 47, 11, 12, 34, 57, 81, 106, 132, 159, 187, 216, 246, 277, 15, 48, 82, 117, 153, 190, 228, 267, 307, 16, 58, 101, 17, 18, 64, 111, 159, 208, 258, 309, 361, 414, 468, 523, 19, 20, 78, 137, 22, 83, 24, 87, 151, 25, 91
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OFFSET

1,2


LINKS



EXAMPLE

a(8) = 6 because a(7) is prime and 6 is the smallest number that has not appeared in the sequence thus far.
a(9) = 6 + 9  1 = 14 because a(8) is not prime.


MATHEMATICA

f[s_] := Module[{k=1, t}, t = If[!PrimeQ[s[[1]]], s[[1]] + Length[s], While[!FreeQ[s, k], k++]; k]; Join[s, {t}]]; Nest[f, {1}, 66] (* Amiram Eldar, Sep 28 2022 *)


PROG

(Python)
from sympy import isprime
from itertools import count, filterfalse
for n in range(1, 100):
if isprime(A[1]):
y = next(filterfalse(set(A).__contains__, count(1)))
else:
y = A[1] + n
A.append(y)


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



