A321058 Indices of records in A067849.

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

Offset: 1

Author

Torlach Rush, Oct 26 2018

Keywords

• nonn
• more

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)

Examples

			2 is a term because A067849(2) = 4 > A067849(1) = 2.
44 is a term because A067849(44) = 6 > A067869(2) = 4.
		

Crossrefs

Cf. A067849, A005602, A057331, A063378.

Programs

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

Extensions

a(7) from Amiram Eldar, Nov 10 2018

a(8)-a(10) from A057331 by Glen Whitney, Sep 14 2022