A275272 -id:A275272 - cp's OEIS frontend

A275273 p - n!, where p is the third smallest prime > n!.

4, 5, 7, 13, 17, 19, 37, 37, 31, 41, 19, 59, 109, 71, 179, 73, 59, 73, 113, 53, 47, 127, 149, 263, 107, 241, 59, 103, 317, 241, 317, 113, 197, 127, 109, 647, 397, 67, 281, 67, 211, 163, 109, 107, 439, 521, 709, 101, 383, 337, 397, 223, 337, 601, 281, 311

Offset: 1

Clark Kimberling, Jul 23 2016

Is every term except 4 a prime?

			For n = 4, we have n! = 24, so that p = 37, and a(4) = 13.

Clark Kimberling, Table of n, a(n) for n = 1..300

Cf. A275272, A000040.

Table[NextPrime[n!, 3] - n!, {n, 1, 150}]
NextPrime[#,3]-#&/@(Range[60]!) (* Harvey P. Dale, Sep 29 2024 *)

A275274 p - n!, where p is the fourth smallest prime > n!.

Original entry on oeis.org

6, 9, 11, 17, 19, 23, 41, 41, 47, 47, 29, 83, 139, 79, 223, 149, 83, 101, 137, 79, 59, 131, 271, 283, 131, 263, 137, 197, 373, 313, 379, 137, 307, 151, 257, 761, 457, 151, 443, 89, 229, 167, 181, 191, 467, 1109, 739, 103, 401, 353, 487, 827, 449, 617, 307

Offset: 1

Clark Kimberling, Jul 23 2016

Is every term except the first two a prime?

			For n = 4, we have n! = 24, so that p = 41, and a(4) = 17.

Clark Kimberling, Table of n, a(n) for n = 1..300

Cf. A275272, A000040.

Table[NextPrime[n!, 4] - n!, {n, 1, 150}]

A275275 n! - p, where p is the second greatest prime < n!.

Original entry on oeis.org

4, 5, 3, 5, 11, 11, 17, 37, 17, 17, 17, 13, 61, 17, 59, 71, 61, 43, 113, 71, 41, 101, 191, 103, 191, 179, 71, 127, 37, 79, 113, 163, 47, 373, 293, 157, 149, 79, 167, 211, 151, 89, 131, 113, 73, 107, 179, 227, 173, 113, 257, 239, 151, 227, 163, 509, 293, 347

Offset: 1

Clark Kimberling, Jul 23 2016

Is every term except 4 a prime?

			For n = 4, we have n! = 24, so that p = 19, and a(4) = 5.

Clark Kimberling, Table of n, a(n) for n = 1..300

Cf. A275272, A000040.

Table[n! - NextPrime[n!, -2], {n, 1, 150}]

A275276 a(n) = n! - p, where p is the third greatest prime less than n!.

Original entry on oeis.org

6, 7, 4, 7, 13, 19, 19, 43, 29, 23, 43, 17, 67, 43, 71, 89, 239, 47, 197, 151, 43, 139, 197, 191, 239, 191, 173, 197, 47, 97, 223, 373, 71, 439, 307, 263, 157, 241, 199, 233, 337, 131, 179, 149, 113, 277, 269, 409, 197, 193, 379, 271, 181, 419, 367, 701, 751

Offset: 1

Clark Kimberling, Jul 23 2016

Is every term except 4 and 6 a prime?

			For n = 4, we have n! = 24, so that p = 17, and a(4) = 7.

Clark Kimberling, Table of n, a(n) for n = 1..300

Cf. A275272, A000040.

Table[n! - NextPrime[n!, -3], {n, 1, 150}]

Name corrected by Pavel Irzhavski, Jul 25 2016

cp's OEIS Frontend

A275273 p - n!, where p is the third smallest prime > n!.

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A275274 p - n!, where p is the fourth smallest prime > n!.

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Mathematica

A275275 n! - p, where p is the second greatest prime < n!.

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Mathematica

A275276 a(n) = n! - p, where p is the third greatest prime less than n!.

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