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 1-3 of 3 results.

A263925 a(n) = least m > 1 such that m + (prime(n)#)^n is prime.

Original entry on oeis.org

3, 5, 11, 19, 89, 323, 29, 61, 79, 199, 563, 181, 353, 1307, 257, 709, 1237, 1277, 1609, 1237, 4157, 2017, 577, 157, 191, 1063, 239, 823, 1607, 4159, 139, 11527, 2339, 18457, 4079, 463, 1861, 1123, 8699, 16561, 719, 4327, 9311, 1693, 3067, 4243, 22397, 4079, 3989, 24071
Offset: 1

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Author

Alexei Kourbatov, Oct 30 2015

Keywords

Comments

Here prime(n)# denotes the primorial A002110(n), i.e., the product of the first n primes. Terms a(n) are often (but not always) prime; out of the first fifty terms, only one (a(6)=323) is composite.
The definition is similar to Fortunate numbers (A005235); however, in A005235 the primorial is not raised to the n-th power. Unlike this sequence, all known Fortunate numbers are prime.

Examples

			(prime(2)#)^2=36. a(2)=5 because 5 is the minimal m>1 such that m+36 is prime.

Crossrefs

Cf. A002110, A005235, A181555, A264050.

Programs

  • Mathematica
    Table[m = 2; While[! PrimeQ[m + Product[Prime@ i, {i, n}]^n], m++]; m, {n, 30}] (* Michael De Vlieger, Nov 11 2015 *)
  • PARI
    a(n)=my(s=prod(i=1,n,prime(i))^n); nextprime(s+2)-s

A268607 a(n) is the least m > 1 such that 2^n - m is prime.

Original entry on oeis.org

2, 3, 3, 3, 3, 15, 5, 3, 3, 9, 3, 13, 3, 19, 15, 9, 5, 19, 3, 9, 3, 15, 3, 39, 5, 39, 57, 3, 35, 19, 5, 9, 41, 31, 5, 25, 45, 7, 87, 21, 11, 57, 17, 55, 21, 115, 59, 81, 27, 129, 47, 111, 33, 55, 5, 13, 27, 55, 93, 31, 57, 25, 59, 49, 5, 19, 23, 19, 35, 231, 93
Offset: 2

Views

Author

Alexei Kourbatov, Feb 08 2016

Keywords

Comments

a(1) is not defined (there are no primes less than 2).
The definition is similar to Lesser Fortunate numbers (A055211) but uses 2^n instead of primorials A002110(n).

Examples

			a(7)=15 because m=15 is the least m > 1 such that 2^7 - m is prime.

Links

Crossrefs

Cf. A005235, A013603, A055211, A264050, A263925, A268608.

Programs

  • Mathematica
    Map[# - NextPrime[#-1, -1] &, 2^Range[2, 100]] (* Paolo Xausa, Mar 10 2025 *)
  • PARI
    a(n)=2^n-precprime(2^n-2)

Formula

a(n) = A013603(n), if A013603(n) > 1. - Jason Yuen, Mar 10 2025

A268608 a(n) is the least m > 1 such that (prime(n)#)^n - m is prime.

Original entry on oeis.org

5, 7, 19, 23, 41, 163, 67, 257, 83, 109, 43, 359, 293, 647, 277, 1567, 983, 419, 1723, 83, 103, 3089, 719, 733, 1723, 457, 331, 2729, 3389, 1123, 863, 1123, 1871, 6211, 19717, 5323, 5749, 419, 887, 811, 617, 2851, 2531, 5023, 6883, 6661, 2879, 16433, 19471
Offset: 2

Views

Author

Alexei Kourbatov, Feb 08 2016

Keywords

Comments

Here prime(n)# denotes the primorial A002110(n), i.e., the product of the first n primes. a(1) is not defined (there are no primes less than 2).
The definition is similar to Lesser Fortunate numbers (A055211) - but here primorials A002110(n) are raised to the n-th power.
Similar to Fortunate numbers (A005235) and Lesser Fortunate numbers (A055211), the first fifty terms are all prime. (Cf. A263925 where the 6th term is composite.)

Examples

			a(2)=5 because m=5 is the least m > 1 such that A002110(2)^2 - m is prime.

Crossrefs

Cf. A002110, A005235, A055211, A264050, A263925, A268607.

Programs

  • PARI
    a(n)=my(s=prod(i=1, n, prime(i))^n); s-precprime(s-2)
Showing 1-3 of 3 results.

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