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 A356188 a(1)=1; for n > 1, if a(n-1) is prime then a(n) = the smallest number not yet in the sequence. Otherwise a(n) = a(n-1) + 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..67. 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 A356188 = A = [1] 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 Cf. A000040, A060735, A073659, A331603. Sequence in context: A060984 A226947 A272615 * A238962 A238975 A098348 Adjacent sequences: A356185 A356186 A356187 * A356189 A356190 A356191 KEYWORD nonn,easy AUTHOR John Tyler Rascoe, Jul 28 2022 STATUS approved

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Last modified May 28 15:56 EDT 2024. Contains 372916 sequences. (Running on oeis4.)