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.

A086519 a(n) is the least prime not already used such that (a(n)+a(n-1))/2 is prime.

Original entry on oeis.org

3, 7, 19, 43, 31, 103, 151, 67, 79, 127, 199, 163, 139, 223, 331, 211, 271, 283, 379, 367, 307, 439, 487, 607, 547, 499, 643, 571, 523, 619, 463, 631, 691, 727, 739, 883, 823, 751, 787, 859, 907, 811, 1063, 919, 1123, 1051, 967, 1171, 1087, 991, 1471, 1291
Offset: 0

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Author

Amarnath Murthy, Jul 30 2003

Keywords

Comments

Second term onwards every prime == 1 (mod 6). Conjecture: every prime of the type 6k+1 is a member.
After the first term, every member = 7 (mod 12). Conjecture: every prime of the form 12k+7 is a member. - David Wasserman, Mar 11 2005

Crossrefs

Cf. A086522.

Extensions

More terms from David Wasserman, Mar 11 2005

A086523 Beginning with 5, distinct odd primes such that the arithmetic mean of every pair of successive terms is prime.

Original entry on oeis.org

5, 17, 29, 53, 41, 101, 113, 149, 197, 257, 269, 293, 401, 461, 521, 593, 641, 653, 701, 821, 857, 1049, 1277, 1289, 1433, 1553, 1613, 1721, 1901, 1913, 1949, 1997, 2081, 2141, 2273, 2393, 2441, 2477, 2609, 2633, 2693, 2729, 2753, 2801, 2837, 2957, 2969
Offset: 1

Views

Author

Amarnath Murthy, Jul 30 2003

Keywords

Comments

Every term == -1 (mod 6).
Conjecture: every prime of the form 6k-1 is a member. Comment from Vim Wenders, May 27 2008: The conjecture is wrong. For example 11 and 23 are missing.

Crossrefs

Cf. A086519, A086522, A086524.

Extensions

More terms from Ray G. Opao, Jan 24 2005

A086524 Primes arising as the arithmetic mean of a pair of successive terms of A086523.

Original entry on oeis.org

11, 23, 41, 47, 71, 107, 131, 173, 227, 263, 281, 347, 431, 491, 557, 617, 647, 677, 761, 839, 953, 1163, 1283, 1361, 1493, 1583, 1667, 1811, 1907, 1931, 1973, 2039, 2111, 2207, 2333, 2417, 2459, 2543, 2621, 2663, 2711, 2741, 2777, 2819, 2897, 2963, 3089
Offset: 1

Views

Author

Amarnath Murthy, Jul 30 2003

Keywords

Comments

Every term == -1 (mod 6). Conjecture: every prime of the form 6k-1 is a member.

Crossrefs

Cf. A086519, A086522, A086523.

Extensions

More terms from Ray G. Opao, Jan 24 2005
Showing 1-3 of 3 results.

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