Search: a290489 -id:a290489
|
| |
|
|
A290488
|
|
Lower ends of record gaps between numbers that are either prime or twice a prime.
|
|
+10
5
|
|
|
|
2, 7, 47, 181, 467, 526, 1069, 1262, 1327, 2477, 3274, 5119, 12854, 20809, 28229, 31397, 338038, 520462, 546391, 1050631, 1761206, 1964987, 3466943, 6084986, 27348829, 27915754, 111108769, 113652443, 230126378, 231902267, 327764081, 438981007, 581755318, 1837981547, 2489382697
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
The gap between 31397 and 31454 is due to the record prime gap between 31397 and 31469 being almost exactly twice the record prime gap between 15683 and 15727.
|
|
|
LINKS
|
|
|
|
FORMULA
|
|
|
|
EXAMPLE
|
a(3) = 47 because the next number that is a prime or twice a prime after 47 is 53, and that is a record gap of size 6.
|
|
|
MATHEMATICA
|
nxt[n_] := Block[{k = n +1}, While[ !PrimeQ[ k] && ! PrimeQ[ k/2], k++]; k]; p = 2; q = 3; mx = 0; lst = {}; While[p < 2500000000, If[q > mx + p, mx = q - p; AppendTo[ lst, p]]; p = q; q = nxt@ q]; lst (* Robert G. Wilson v, Aug 03 2017 *)
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
| |
|
|
A290541
|
|
Record gaps between numbers that are either prime or twice a prime.
|
|
+10
3
|
|
|
|
1, 3, 6, 10, 11, 12, 13, 15, 19, 21, 25, 28, 35, 40, 48, 57, 60, 64, 70, 75, 83, 90, 95, 117, 120, 144, 148, 150, 153, 167, 168, 196, 205, 212, 214, 221, 234, 244, 254, 255
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
The gap of 57 between 31397 and 31454 is due to the record prime gap between 31397 and 31469 being almost exactly twice the record prime gap between 15683 and 15727.
|
|
|
LINKS
|
|
|
|
FORMULA
|
|
|
|
EXAMPLE
|
a(3) = 6 because the next number that is a prime or twice a prime after 47 is 53, and that is a record gap of size 6.
|
|
|
MATHEMATICA
|
With[{nn = 10^7}, Union@ FoldList[Max, Differences@ #] &@ Union@ Flatten@ {#, 2 TakeWhile[#, # < Prime[nn]/2 &]} &@ Prime@ Range@ nn] (* Michael De Vlieger, Aug 06 2017 *)
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
more,nonn
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
| |
| |
|
|
|
1, 1, 1, 1, 1, 3, 1, 2, 1, 3, 2, 3, 1, 3, 3, 2, 3, 3, 1, 3, 2, 3, 1, 6, 5, 1, 2, 1, 5, 4, 2, 1, 5, 3, 1, 3, 3, 5, 3, 4, 2, 3, 1, 2, 4, 5, 4, 5, 4, 3, 3, 2, 3, 4, 3, 2, 6, 1, 5, 3, 1, 6, 5, 1, 2, 10, 2, 1, 3, 2, 3, 4, 5, 3, 4, 5, 3, 1, 2, 4, 6, 2, 10, 3, 3, 5, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,6
|
|
|
LINKS
|
|
|
|
MATHEMATICA
|
With[{nn = 56}, Differences@ Union@ Flatten@ {#, 2 TakeWhile[#, # < Prime[nn]/2 &]} &@ Prime@ Range@ nn]
|
|
|
PROG
|
(PARI) lista(nn) = {last = 2; for (n=3, nn, if (isprime(n) || (!(n%2) && isprime(n/2)), print1(n - last, ", "); last = n; ); ); }
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
| |
|
|
A290572
|
|
Least number that is the start of a gap of size n between numbers that are either prime or twice a prime (A001751).
|
|
+10
1
|
|
|
|
2, 11, 7, 67, 53, 47, 514, 401, 317, 181, 467, 526, 1069, 2819, 1262, 3142, 1382, 1913, 1327, 4178, 2477, 9697, 8123, 8329, 3274, 11213, 21031, 5119, 16382, 13063, 20446, 44417, 22193, 37747, 12854, 46957, 35617, 63863, 48679, 20809, 76166, 39251, 110359, 59282, 136898, 212923, 143006
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
Numbers that are less than any later number are recorded in A290488.
|
|
|
LINKS
|
|
|
|
EXAMPLE
|
a(1) is 2 since 3 - 2 = 1;
a(2) is 11 since 13 - 11 = 2;
a(3) is 7 since 10 - 7 = 3;
a(4) is 67 since 71 - 67 = 4; etc.
|
|
|
MATHEMATICA
|
nxt[n_] := Block[{k = n +1}, While[ !PrimeQ[k] && !PrimeQ[k/2], k++]; k]; p = 2; q = 3; t[_] = 0; While[p < 215000, d = q - p; If[ t[d] == 0, t[d] = p]; p = q; q = nxt@ q]; t@# & /@ Range@ 47
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
Search completed in 0.005 seconds
|
