A350825
Number of prime 5-tuples with initial member (A086140) between 10^(n-1) and 10^n.
Original entry on oeis.org
2, 2, 1, 4, 12, 44, 256, 1062, 5838
Offset: 1
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.
Cf.
A086140 (initial members p of prime quintuplets),
A022006,
A022007 (idem, specifically for patterns (p, p+2, ...) resp. (p, p+4, ...)).
A350827
Number of prime septuplets (i.e.: 7-tuples) with initial member (A022009 or A022010) between 10^(n-1) and 10^n.
Original entry on oeis.org
0, 1, 0, 1, 1, 4, 5, 21, 70, 370, 1862, 9634
Offset: 1
a(1) = a(3) = 0 because there is no single-digit nor a 3-digit prime to start a prime septuplet.
a(2) = a(4) = a(5) = 1 because 11 = A022009(1), 5639 = A022010(1) and 88799 = A022010(2) are the only prime with 2, 4 resp. 5 digits to start a prime septuplet.
Then there are a(6) = 4 six-digit primes, 165701, 284729, 626609 and 855719, which start a prime septuplet.
Cf.
A022009,
A022010: initial members p of prime septuplets (p, p+2, p+6, ...) resp. (p, p+2, p+8, ...).
-
apply( {A350827(n,v=vector(6),c)=forprime(p=10^(n-1),10^n, v[n=1+n%#v]+20==(v[n]=p) && c++);c}, [1..8]) \\ becomes slow for n > 8. - M. F. Hasler, Apr 12 2022
A350829
Number of prime 9-tuples (or: nonuplets) with initial member (A257125) between 10^(n-1) and 10^n.
Original entry on oeis.org
1, 3, 0, 1, 1, 3, 0, 1, 8, 30, 88
Offset: 1
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.
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.
Showing 1-3 of 3 results.
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