A113831
Last term of a 2 X n generalized arithmetic progression (GAP) of primes with smallest last term.
Original entry on oeis.org
13, 43, 59, 227, 353, 1439, 4969, 5179
Offset: 2
Here is the beginning of Granville's table:
n GAP Last term
2 3+8i+2j 13
3 7+24i+6j 43
4 5+36i+6j 59
5 11+96i+30j 227
6 11+42i+60j 353
7 47+132i+210j 1439
A273919
Number of 9-tuples of primes in arithmetic progression less than 10^n.
Original entry on oeis.org
0, 0, 0, 3, 57, 984, 22551
Offset: 1
The least 9-tuple is {199, 409, 619, 829, 1039, 1249, 1459, 1669, 1879}, which is also the beginning of the least 10-tuple. This explains a(n)=0 for n<4.
Cf.
A113827 (prime beginning minimal n-tuple of primes in AP).
Cf.
A005115,
A115608,
A115609,
A115610,
A115611,
A115612,
A115613,
A273920,
A273921,
A273922,
A273923.
A273920
Number of 10-tuples of primes in arithmetic progression less than 10^n.
Original entry on oeis.org
0, 0, 0, 1, 5, 145, 2969
Offset: 1
The least 10-tuple is {199, 409, 619, 829, 1039, 1249, 1459, 1669, 1879, 2089}, which explains a(4)=1 (and a(n)=0 for n<4).
Cf.
A113827 (prime beginning minimal n-tuple of primes in AP).
Cf.
A005115,
A115608,
A115609,
A115610,
A115611,
A115612,
A115613,
A273919,
A273921,
A273922,
A273923.
A273921
Number of 11-tuples of primes in arithmetic progression less than 10^n.
Original entry on oeis.org
0, 0, 0, 0, 0, 15, 253, 5561
Offset: 1
The least 11-tuple is {110437, 124297, 138157, 152017, 165877, 179737, 193597, 207457, 221317, 235177, 249037} (this is also the beginning of the least 12-tuple). This is one of the 15 11-tuples corresponding to a(6)=15.
Cf.
A113827 (prime beginning minimal n-tuple of primes in AP).
Cf.
A005115,
A093364,
A115608,
A115609,
A115610,
A115611,
A115612,
A115613,
A273919,
A273920,
A273922,
A273923.
A273922
Number of 12-tuples of primes in arithmetic progression less than 10^n.
Original entry on oeis.org
0, 0, 0, 0, 0, 6, 42, 715
Offset: 1
The least 12-tuple is {110437, 124297, 138157, 152017, 165877, 179737, 193597, 207457, 221317, 235177, 249037, 262897}.
Cf.
A113827 (prime beginning minimal n-tuple of primes in AP).
Cf.
A005115,
A093364,
A115608,
A115609,
A115610,
A115611,
A115612,
A115613,
A273919,
A273920,
A273921,
A273923.
A273923
Number of 13-tuples of primes in arithmetic progression less than 10^n.
Original entry on oeis.org
0, 0, 0, 0, 0, 1, 3, 52
Offset: 1
The least 13-tuple is {4943, 65003, 125063, 185123, 245183, 305243, 365303, 425363, 485423, 545483, 605543, 665603, 725663}.
Cf.
A113827 (prime beginning minimal n-tuple of primes in AP).
Cf.
A005115,
A093364,
A115608,
A115609,
A115610,
A115611,
A115612,
A115613,
A273919,
A273920,
A273921,
A273922.
A113830
Leading term of a 2 X n generalized arithmetic progression (GAP) of primes with smallest last term.
Original entry on oeis.org
3, 7, 5, 11, 11, 47, 199, 199
Offset: 2
Here is the beginning of Granville's table:
n GAP Last term
2 3+8i+2j 13
3 7+24i+6j 43
4 5+36i+6j 59
5 11+96i+30j 227
6 11+42i+60j 353
7 47+132i+210j 1439
A113833
Triangle read by rows: row n (n>=2) gives a set of n primes such that the averages of all subsets are distinct primes, having the smallest largest element.
Original entry on oeis.org
3, 7, 7, 19, 67, 5, 17, 89, 1277, 209173, 322573, 536773, 1217893, 2484733
Offset: 2
Triangle begins:
3, 7
7, 19, 67
5, 17, 89, 1277
- Antal Balog, The prime k-tuplets conjecture on average, in "Analytic Number Theory" (eds. B. C. Berndt et al.) Birkhäuser, Boston, 1990, pp. 165-204. [Background]
A279062
Initial terms of the arithmetic progressions in A278735.
Original entry on oeis.org
3, 3, 5, 353, 13297, 1561423, 291461857
Offset: 1
a(4) = 353 because 353 = prime(prime(20)), 431 = prime(prime(23)), 509 = prime(prime(25)), 587 = prime(prime(28)), and 431-353 = 509-431 = 587-509 = 78.
The corresponding arithmetic progressions are
3;
3, 5;
5, 11, 17;
353, 431, 509, 587;
13297, 21937, 30577, 39217, 47857;
1561423, 2716423, 3871423, 5026423, 6181423, 7336423;
...
A269905
Smallest of n^2 primes in an arithmetic progression that form an n X n magic square with the least magic sum, or 0 if no such magic square exists.
Original entry on oeis.org
2, 0, 199, 53297929
Offset: 1
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