|
| |
|
|
A308987
|
|
In the sequence {n^2+1} (A002522), color the primes red. When the number of terms m between successive red terms sets a new record, write down m+1.
|
|
1
|
|
|
|
1, 2, 4, 10, 14, 16, 20, 34, 40, 46, 88, 100, 112, 130, 152, 212, 288, 330, 346, 444, 502, 526, 534, 564, 580, 614, 624, 634, 636, 640, 690
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
This sequence represents the highest gaps, given by number of terms (including the starting prime) in sequence A002522 between terms which are prime.
|
|
|
LINKS
|
Table of n, a(n) for n=1..31.
|
|
|
EXAMPLE
|
n=6 --> 6^2+1 = 37, prime
n=7 --> 7^2+1 = 50, composite
n=8 --> 8^2+1 = 65, composite
n=9 --> 9^2+1 = 82, composite
n=10 --> 10^2+1 = 101, prime
...so here m=3 and we get the third term, m + 1 = 10 - 6 = 4
|
|
|
MATHEMATICA
|
best = c = lastBestAt = 0;
For[i = 2, True, i += 2; c += 2,
If[PrimeQ[i^2 + 1],
If[c > best,
best = c;
bestAt = i - c;
If[bestAt != lastBestAt, Print[{c, bestAt}]];
lastBestAt = bestAt;
];
c = 0;
]
]
|
|
|
CROSSREFS
|
Cf. A002496, A002522, A308988.
A293564 gives essentially the same information.
Sequence in context: A034233 A056718 A057283 * A107992 A139480 A227388
Adjacent sequences: A308984 A308985 A308986 * A308988 A308989 A308990
|
|
|
KEYWORD
|
nonn,more
|
|
|
AUTHOR
|
Trevor Cappallo, Jul 04 2019
|
|
|
EXTENSIONS
|
a(21)-a(31) from Giovanni Resta, Jul 05 2019
|
|
|
STATUS
|
approved
|
| |
|
|
