A321058 Indices of records in A067849.

1, 2, 44, 561329, 9549959, 42932384, 13044904289, 277344139214, 2045466215756534, 47702521115271164

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: A161745 A048566 A374293 * 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