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.

A087899 Primes associated with A087898.

Original entry on oeis.org

5, 29, 389, 8969, 331889, 17590169, 1178541389, 93104769809, 14617448860169, 2528818652809409, 483004362686597309, 95151859449259670069, 26357065067444928609389, 7406335283952024939238589, 3414320565901883496988989989, 1635459551067002195057726205209
Offset: 1

Views

Author

Lekraj Beedassy, Oct 14 2003

Keywords

Links

Crossrefs

Cf. A087898.

Programs

  • Mathematica
    s = {}; ps = {2}; Do[r = Times @@ ps; p = ps[[-1]]; While[p = NextPrime[p]; ! PrimeQ[r*p - 1]]; AppendTo[ps, p]; AppendTo[s, r*p - 1], {15}]; s (* Amiram Eldar, Jan 19 2023 *)

Formula

a(n) = -1 + Product_{k=1..n-1} A087898(k).
a(n) == 9 (mod 10) for n>1. - Sam Alexander, Jan 06 2005

Extensions

a(14) from Sam Alexander, Jan 06 2005
More terms from Amiram Eldar, Jan 19 2023

A290427 Rearrangement of primes such that every partial product minus 1 is a prime.

Original entry on oeis.org

3, 2, 5, 13, 7, 11, 19, 43, 79, 31, 17, 71, 89, 23, 41, 67, 29, 73, 83, 107, 59, 53, 239, 101, 109, 233, 61, 197, 97, 103, 37, 211, 113, 157, 167, 131, 181, 179, 269, 127, 421, 47, 523, 173, 331, 307, 149, 347, 257, 199, 277, 139, 151, 433, 223, 449, 227, 313, 647, 443, 283, 929, 509
Offset: 1

Views

Author

Robert G. Wilson v, Jul 31 2017

Keywords

Comments

Records: 3, 5, 13, 19, 43, 79, 89, 107, 239, 269, 421, 523, 647, 929, 1069, 1321, 1783, 1879, 2347, 4217, 4801, 7001, 7691, 9623, 22769, 23011, 27541, 29009, ..., .
Position of the n_th prime: 2, 1, 3, 5, 6, 4, 11, 7, 14, 17, 10, 31, 15, 8, 42, 22, 21, 27, 16, 12, 18, 9, ..., .
Prime index of a(n): 2, 1, 3, 6, 4, 5, 8, 14, 22, 11, 7, 20, 24, 9, 13, 19, 10, 21, 23, 28, 17, 16, 52, 26, 29, 51, ..., .

Links

Crossrefs

Cf. A000040, A087898, A083771.

Programs

  • Mathematica
    f[s_List] := Block[{p = Times @@ s, q = 2}, While[ MemberQ[s, q] || !PrimeQ[p*q - 1], q = NextPrime@ q]; Append[s, q]]; Nest[f, {3}, 40]

Formula

3*2*5*...*a(n) -1 is prime. a(n) is the least prime not previously in the sequence.

A359939 Lexicographically earliest strictly increasing sequence of primes whose partial products lie between noncomposite numbers.

Original entry on oeis.org

2, 3, 5, 19, 41, 67, 113, 653, 883, 1439, 3823, 10631, 12841, 14251, 23357, 27103, 30491, 64679, 78823, 110977, 115127, 118747, 159431, 215587, 301039, 342257, 343639, 428401, 473383, 493583, 566723, 621133, 638371, 639157, 680539, 904049, 993037, 1146133, 1252507
Offset: 1

Views

Author

Amiram Eldar, Jan 19 2023

Keywords

Examples

			2 - 1 = 1 and 2 + 1 = 3 are both noncomposite numbers.
2*3 - 1 = 5 and 2*3 + 1 = 7 are both noncomposite numbers.
2*3*5 - 1 = 29 and 2*3*5 + 1 = 31 are both noncomposite numbers.

Links

Crossrefs

Cf. A008578, A014574, A039726, A087898, A167777, A359940.

Programs

  • Mathematica
    a[1] = 2; a[n_] := a[n] = Module[{r = Product[a[k],{k, 1, n-1}], p = NextPrime[a[n-1]]}, While[!PrimeQ[r*p-1] || !PrimeQ[r*p+1], p = NextPrime[p]]; p]; Array[a, 50]
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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