A350825 Number of prime 5-tuples with initial member (A086140) between 10^(n-1) and 10^n.

2, 2, 1, 4, 12, 44, 256, 1062, 5838

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 digits".

For n = 1 and n = 2, the last term of the last 5-tuple in that range (cf EXAMPLE) has one digit more than the initial term.

Terms a(1)-a(9) computed from b-files a(1..10000) for A022006 and A022007.

Examples

			a(1) = 2 because there are just two single-digit primes to start a prime 5-tuple, namely 5 = A022006(1) and 7 = A022007(1).
a(2) = 2 because 11 = A022006(2) and 97 = A022007(2) are the only two two-digit primes to start a prime 5-tuple.
a(3) = 1 because there is only one three-digit prime to start a prime 5-tuple, namely 101 = A022006(3).
Then there are a(4) = 4 four-digit primes, 1481, 1867, 3457 and 5647, which start a prime 5-tuple.
		

Crossrefs

Cf. A086140 (initial members p of prime quintuplets), A022006, A022007 (idem, specifically for patterns (p, p+2, ...) resp. (p, p+4, ...)).

Cf. A350826, A350827, A350828: similar for sextuplets, septuplets and octuplets.

Programs

PARI

(D(v)=v[^1]-v[^-1])( [setsearch(A086140, 10^n, 1) | n<-[0..9]] ) \\ where A086140 is a vector of at least 7221 terms of that sequence.