A113831 -id:A113831 - cp's OEIS frontend

A113832 Triangle read by rows: row n (n>=2) gives a set of n primes with the property that the pairwise averages are all primes, having the smallest largest element.

3, 7, 3, 7, 19, 3, 11, 23, 71, 5, 29, 53, 89, 113, 3, 11, 83, 131, 251, 383, 5, 29, 113, 269, 353, 449, 509, 5, 17, 41, 101, 257, 521, 761, 881, 23, 431, 503, 683, 863, 1091, 1523, 1871, 2963, 31, 1123, 1471, 1723, 3463, 3571, 4651, 5563, 5743, 6991

Offset: 2

N. J. A. Sloane, Jan 25 2006

If there is more than one set with the same smallest last element, choose the lexicographically earliest solution.

For distinct primes, the solution for n=5 is {5, 29, 53, 89, 173}.

			Triangle begins:
3, 7
3, 7, 19
3, 11, 23, 71
5, 29, 53, 89, 113
3, 11, 83, 131, 251, 383
5, 29, 113, 269, 353, 449, 509
The set of primes generated by {5, 29, 53, 89, 113} is {17, 29, 41, 47, 59, 59, 71, 71, 83, 101}.

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]

Toshitaka Suzuki, Table of n, a(n) for n = 2..91
Jens Kruse Andersen, Primes in Arithmetic Progression Records [May have candidates for later terms in this sequence.]
Andrew Granville, Prime number patterns

Cf. A113827-A113831, A113833, A113834, A088430.

See A115631 for the case when all pairwise averages are distinct primes.

More terms from T. D. Noe, Feb 01 2006

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

N. J. A. Sloane, Jan 25 2006

			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

Jens Kruse Andersen, Primes in Arithmetic Progression Records [May have candidates for later terms in this sequence.]
Andrew Granville, Prime number patterns

Cf. A113831, A113827, A113828, A005150.

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

N. J. A. Sloane, Jan 25 2006

If there is more than one set with the same smallest last element, choose the lexicographically earliest solution.

Note that, in each row, the n primes are equal modulo 4, 12, 12 and 120, respectively. - Row 5 from T. D. Noe, Aug 08 2006

			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]

Jens Kruse Andersen, Primes in Arithmetic Progression Records [May have candidates for later terms in this sequence.]
Andrew Granville, Prime number patterns

Cf. A113827-A113831, A113832, A113834, A088430.

Row 5 from T. D. Noe, Aug 08 2006

A153412 Differences in the first known 3 X 3 X 3 generalized arithmetic progression consisting of only prime numbers.

Original entry on oeis.org

2904, 3150, 7440

Offset: 1

Jonathan Vos Post, Dec 25 2008

Andrew Granville, Prime Number Patterns, American Mathematical Monthly, April 2008.
MAA, Students Uncover a Novel Prime Progression, November 25, 2008.

Cf. A113830, A113831.

cp's OEIS Frontend

A113832 Triangle read by rows: row n (n>=2) gives a set of n primes with the property that the pairwise averages are all primes, having the smallest largest element.

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A113830 Leading term of a 2 X n generalized arithmetic progression (GAP) of primes with smallest last term.

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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.

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Extensions

A153412 Differences in the first known 3 X 3 X 3 generalized arithmetic progression consisting of only prime numbers.

Views

Author

Keywords

Links

Crossrefs