A350829 Number of prime 9-tuples (or: nonuplets) with initial member (A257125) between 10^(n-1) and 10^n.

1, 3, 0, 1, 1, 3, 0, 1, 8, 30, 88

Offset: 1

Author

M. F. Hasler, Mar 01 2022

Keywords

• nonn
• base
• hard
• more

Comments

"Between 10^(n-1) and 10^n" is equivalent to saying "with n (decimal) digits".

A prime nonuplet is a sequence of 9 consecutive primes (p1, ..., p9) of minimal diameter p9 - p1 = 30.

Terms a(1)-a(11) computed from b-file a(1..651) for A257125.

Apart for n = 1 (cf. EXAMPLE), so far the last term of all the nonuplets has the same number of digits as the initial term.

Examples

			a(1) = 1 because 7 is the only single-digit prime to start a prime nonuplet, i.e., member of A257125. (All other members of this nonuplet have 2 digits.)
a(2) = 3 because 11, 13 and 17 are the three 2-digit primes to start a prime nonuplet.
a(3) = 0 because there is no 3-digit prime initial member of a prime nonuplet.
		

Crossrefs

Cf. A257125 (initial members p of prime nonuplets (p, ..., p+30)), A022545 - A022548 (idem, specifically for each of the four possible patterns).

Cf. A350825 - A350828: similar for quintuplets, sextuplets, septuplets and octuplets.

Programs

PARI

(D(v)=v[^1]-v[^-1])( [setsearch(A257125,10^n,1) | n<-[0..12]] ) \\ where A257125 is a vector of at least 3660 terms of that sequence.