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 1-2 of 2 results.

A208662 Smallest m such that the n-th odd prime is the smallest prime for all decompositions of 2*m into two primes.

Original entry on oeis.org

3, 6, 15, 62, 61, 209, 49, 110, 173, 154, 637, 572, 481, 278, 1256, 1763, 691, 928, 2309, 496, 1909, 3716, 6389, 2989, 13049, 1321, 11633, 5134, 9848, 3004, 17096, 11303, 2686, 18884, 6781, 4798, 11416, 29957, 3713, 44393, 25156, 48884, 24001, 56279, 30031
Offset: 1

Views

Author

Reinhard Zumkeller, Feb 29 2012

Keywords

Comments

A002373(a(n)) = A065091(n) and A002373(m) != A065091(n) for m < a(n).

Examples

			n=3, a(3)=15: 7 is the 3rd odd prime and the smallest prime in all Goldbach decompositions of 2*15 = 30 = {7+23, 11+19, 13+17}, and 7 doesn't occur as smallest prime in all Goldbach decompositions for even numbers less than 30.

Links

Crossrefs

Cf. A002373, A065091, A260485.

Programs

  • Haskell
    a208662 n = head [m | m <- [1..], let p = a065091 n,
   let q = 2 * m - p, a010051' q == 1,
   all ((== 0) . a010051') $ map (2 * m -) $ take (n - 1) a065091_list]
-- Reinhard Zumkeller, Aug 11 2015, Feb 29 2012

A260580 Table read by rows: n-th row contains numbers not occurring earlier, that can be written as (p+q)/2 where p is the n-th odd prime, q <= p.

Original entry on oeis.org

3, 4, 5, 6, 7, 8, 9, 11, 10, 12, 13, 14, 15, 17, 16, 18, 19, 20, 21, 23, 24, 26, 29, 22, 25, 27, 30, 31, 28, 33, 34, 37, 32, 35, 36, 39, 41, 40, 42, 43, 38, 44, 45, 47, 48, 50, 53, 51, 56, 59, 46, 49, 52, 54, 57, 60, 61, 55, 63, 64, 67, 62, 65, 66, 69, 71
Offset: 1

Views

Author

Reinhard Zumkeller, Aug 11 2015

Keywords

Comments

Length of n-th row = A105047(n+1);
T(n,1) = A260485(n);
T(n,A105047(n)) = A065091(n).

Examples

			Let p(n) = A065091(n) = prime(n+1):
.   n | p(n) | T(n,*)
. ----+------+----------------- ------------------------------------------
.   1 |    3 | [3]              3
.   2 |    5 | [4,5]            (5+3)/2,5
.   3 |    7 | [6,7]            (7+5)/2,7
.   4 |   11 | [8,9,11]         (11+5)/2,(11+7)/2,11
.   5 |   13 | [10,12,13]       (13+7)/2,(13+11)/2,13
.   6 |   17 | [14,15,17]       (17+11)/2,(17+13)/2,17
.   7 |   19 | [16,18,19]       (19+13)/2,(19+17)/2,19
.   8 |   23 | [20,21,23]       (23+17)/2,(23+19)/2,23
.   9 |   29 | [24,26,29]       (29+19)/2,(29+17)/2,29
.  10 |   31 | [22,25,27,30,31] (31+13)/2,(31+19)/2,(31+23)/2,(31+29)/2,31
.  11 |   37 | [28,33,34,37]    (37+19)/2,(37+29)/2,(37+31)/2,37
.  12 |   41 | [32,35,36,39,41] (41+23)/2,(41+29)/2,(41+31)/2,(41+37)/2,41

Links

Crossrefs

Cf. A065305, A105047, A065091.

Programs

  • Haskell
    import Data.List.Ordered (union); import Data.List ((\\))
a260580 n k = a260580_tabf !! (n-1) !! (k-1)
a260580_row n = a260580_tabf !! (n-1)
a260580_tabf = zipWith (\\) (tail zss) zss where
                            zss = scanl union [] a065305_tabl
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.