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 A321058 Indices of records in A067849. 1
 1, 2, 44, 561329, 9549959, 42932384, 13044904289, 277344139214, 2045466215756534, 47702521115271164 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The corresponding record values are 2,4,6,7,8,9,10,12,13,14. From David A. Corneth, Nov 10 2018: (Start) Terms a(n) are of the form 3*k+2 for n > 1. If 2^k - 1 is composite then a(n) is not divisible by any prime factor of 2^k-1 for n > k. So for example, gcd(a(n), 105) = 1 for n > 5. (End) From Glen Whitney, Sep 14 2022: (Start) Similarly to Corneth's observations, modulo any prime p, any residue for a(n) of the form 2^k - 1 mod p is forbidden for n greater than or equal to the number of such residues; for example a(n) may not be congruent to 0, 1, or 3 mod 7 for n >= 3. For n > 2, if a(n) appears in this sequence, 2a(n) + 1 must appear in A057331. (End) LINKS Table of n, a(n) for n=1..10. EXAMPLE 2 is a term because A067849(2) = 4 > A067849(1) = 2. 44 is a term because A067849(44) = 6 > A067869(2) = 4. PROG (PARI) b(n) = {my(nb = 0, newn); while (isprime(newn=2*n+1), nb++; n = newn); nb; } \\ A067849 lista(nn) = {my(mmax = -1, mm); for (n=1, nn, if ((mm=b(n)) > mmax, mmax = mm; print1(n, ", ")); ); } \\ Michel Marcus, Nov 10 2018 CROSSREFS Cf. A067849, A005602, A057331, A063378. Sequence in context: A291808 A161745 A048566 * A342827 A264438 A241762 Adjacent sequences: A321055 A321056 A321057 * A321059 A321060 A321061 KEYWORD nonn,more AUTHOR Torlach Rush, Oct 26 2018 EXTENSIONS a(7) from Amiram Eldar, Nov 10 2018 a(8)-a(10) from A057331 by Glen Whitney, Sep 14 2022 STATUS approved

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Last modified April 17 17:00 EDT 2024. Contains 371765 sequences. (Running on oeis4.)