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 A284188 a(1)=2; thereafter a(n+1) = a(n)+i if a(n) is a prime and a(1),...,a(n) contains i primes, or a(n+1) = a(n)-i if a(n) is composite and a(1),...,a(n) contains i primes. 2
 2, 3, 5, 8, 5, 9, 5, 10, 5, 11, 18, 11, 19, 28, 19, 29, 40, 29, 41, 54, 41, 55, 41, 56, 41, 57, 41, 58, 41, 59, 78, 59, 79, 100, 79, 101, 124, 101, 125, 101, 126, 101, 127, 154, 127, 155, 127, 156, 127, 157, 188, 157, 189, 157, 190, 157, 191, 226, 191, 227, 264, 227, 265 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Without repeated terms, the primes appear in order as A070865. Variant of A284172; the difference is that in A284172, a(n+1) = a(n)-i if a(n) is composite and a(1),...,a(n) contains i composites (rather than i primes). For n >= 3: When a(n) = prime p it is followed by an even number j at a(n+1); p repeats k-j times (where k is the smallest prime > j), appearing at a(n+2m) {m=1..k-j}. a(n+2m+1) = p+m until p+m = k (immediately following the final p); k now becomes "new p" immediately followed by a "new j", and the process repeats. LINKS Alois P. Heinz, Table of n, a(n) for n = 1..100000 Michael De Vlieger, Log-log scatterplot of a(n) for n=1..2^16. Michael De Vlieger, Log-log scatterplot of a(n) for n=1..2^12, showing a(n) in red and A284172(n) in blue, accentuating the first 12 terms of A284172(n) by enlargement. EXAMPLE a(10) = 11; there are 7 primes in the sequence up to and including a(10) so a(11) = 11+7 = 18. 18 is composite so a(12) = 18-7 = 11. Now there are 8 primes in the sequence; and since 11 is prime, a(13) = 11+8 = 19 (the 9th prime in the sequence), so a(14) = 28. MAPLE c:= proc(n) option remember; `if`(n<1, 0, `if`(isprime(a(n)), 1, 0)+c(n-1)) end: a:= proc(n) option remember; `if`(n=1, 2, (m-> `if`(isprime(m), 1, -1)*c(n-1)+m)(a(n-1))) end: seq(a(n), n=1..100); # Alois P. Heinz, Apr 15 2017 MATHEMATICA Block[{c = 1, m = 2, n}, {2}~Join~Reap[Do[If[PrimeQ[m], Set[n, m + c]; c++, Set[n, m - c + 1]]; Sow[n]; m = n, 63]][[-1, -1]]] (* Michael De Vlieger, Oct 20 2021 *) PROG (PARI) lista(nn) = {print1(a=2, ", "); nbp = 1; for (n=2, nn, if (isprime(a), a += nbp, a -= nbp); print1(a, ", "); if (isprime(a), nbp++); ); } \\ Michel Marcus, Mar 24 2017 CROSSREFS Cf. A070865, A284172. Sequence in context: A191450 A257122 A249188 * A011158 A104647 A065115 Adjacent sequences: A284185 A284186 A284187 * A284189 A284190 A284191 KEYWORD nonn AUTHOR Bob Selcoe, Mar 21 2017 STATUS approved

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Last modified September 18 06:56 EDT 2024. Contains 375996 sequences. (Running on oeis4.)