cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A092945 Group the natural numbers so that the n-th group contains n numbers whose sum as well as the group product + 1 is prime. Sequence contains the last term of each group.

Original entry on oeis.org

2, 4, 10, 9, 23, 28, 29, 47, 115, 71, 88, 214, 215, 188, 341, 133, 220, 372, 250, 321, 227, 311, 281, 310, 592, 857, 691, 406, 470, 483, 904, 903, 707, 601, 876, 727, 726, 1299, 828, 925, 1217, 1254, 963, 1426, 1213, 1394, 2108, 1356, 1448, 1286, 1564, 1455
Offset: 1

Views

Author

Amarnath Murthy, Mar 23 2004

Keywords

Comments

Sequence is underdefined. The original author may have intended to say that the terms must be distinct and minimal; perhaps he should clarify. - Jonathan Vos Post, Mar 22 2006
See A092944 for additional clarification of definition.

Examples

			a(6) = 28 because 15+16+17+18+19+28 = 113 is prime and 15*16*17*18*19*28 + 1 = 39070081 is prime.

Crossrefs

Cf. A092944, A092946, A092947.

Extensions

a(6) from Jonathan Vos Post, Mar 22 2006
Edited and extended by Ray Chandler, May 07 2008

A092944 Group the natural numbers so that the n-th group contains n numbers whose sum as well as the group product + 1 is prime. Sequence contains the first member of the groups.

Original entry on oeis.org

2, 1, 3, 5, 11, 15, 20, 27, 36, 44, 54, 64, 76, 89, 102, 117, 132, 149, 166, 184, 204, 228, 249, 272, 296, 323, 349, 376, 403, 432, 461, 493, 524, 556, 589, 625, 660, 697, 737, 775, 814, 855, 898, 943, 987, 1031, 1076, 1122, 1169, 1219, 1269, 1321, 1373, 1427
Offset: 1

Views

Author

Amarnath Murthy, Mar 23 2004

Keywords

Comments

The n-th group is chosen so that it is lexicographically earliest.
First n-2 numbers are the least previously unused numbers.
The (n-1)st number is chosen with the additional condition that if the product is odd, the sum is also odd (to avoid an impossible situation in picking the n-th number).
The n-th number is chosen as the least unused number that meets the two prime conditions.
In the 3rd group, 6 is selected as the 2nd number rather than 5, else no 3rd number could be found to meet the prime conditions.

Examples

			Table begins:
2
1,4
3,6,10
5,7,8,9
11,12,13,14,23
15,16,17,18,19,28

Crossrefs

Cf. A092945, A092946, A092947.

Extensions

Edited and extended by Ray Chandler, May 07 2008

A092946 Group the natural numbers so that the n-th group contains n numbers whose sum as well as the group product +1 is prime. Sequence contains the primes arising as the sum of the terms of groups.

Original entry on oeis.org

2, 5, 19, 29, 73, 113, 167, 269, 431, 509, 673, 977, 1193, 1423, 1861, 1993, 2467, 3041, 3391, 4003, 4523, 5309, 6011, 6833, 7993, 9239, 10093, 10909, 12157, 13417, 15199, 16651, 17971, 19477, 21517, 23197, 25121, 27799, 29537, 31891, 34583, 37189
Offset: 1

Views

Author

Amarnath Murthy, Mar 23 2004

Keywords

Comments

See A092944 for additional clarification of definition.

Crossrefs

Cf. A092944, A092945, A092947.

Extensions

Edited and extended by Ray Chandler, May 07 2008
Showing 1-3 of 3 results.

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