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.
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;
]
]
Join[{1, 2}, Rest[DeleteDuplicates[Length/@SplitBy[(Range[5*10^7]^2+1), PrimeQ], GreaterEqual]+1]] (* The program generates the first 19 terms of the sequence. *)(* Harvey P. Dale, Sep 27 2024 *)
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Trevor Cappallo, Jul 04 2019
EXTENSIONS
a(21)-a(31) from Giovanni Resta, Jul 05 2019
STATUS
approved