login
A350825
Number of prime 5-tuples with initial member (A086140) between 10^(n-1) and 10^n.
4
2, 2, 1, 4, 12, 44, 256, 1062, 5838
OFFSET
1,1
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.
EXAMPLE
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.
PROG
(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.
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.
Sequence in context: A101560 A307456 A291260 * A218529 A192456 A226948
KEYWORD
nonn,base,hard,more
AUTHOR
M. F. Hasler, Mar 01 2022
STATUS
approved