

A321058


Indices of records in A067849.


1




OFFSET

1,2


COMMENTS

The corresponding record values are 2,4,6,7,8,9,10,12,13,14.
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^k1 for n > k. So for example, gcd(a(n), 105) = 1 for n > 5. (End)
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



EXAMPLE



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



KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



