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.

A336851 a(n) = sigma(A003961(n)) - A003961(n), where A003961 is a prime shift towards larger primes, sigma is the sum of divisors.

Original entry on oeis.org

0, 1, 1, 4, 1, 9, 1, 13, 6, 11, 1, 33, 1, 15, 13, 40, 1, 49, 1, 41, 17, 17, 1, 105, 8, 21, 31, 57, 1, 87, 1, 121, 19, 23, 19, 178, 1, 27, 23, 131, 1, 123, 1, 65, 73, 33, 1, 321, 12, 81, 25, 81, 1, 249, 21, 183, 29, 35, 1, 309, 1, 41, 97, 364, 25, 141, 1, 89, 35, 153, 1, 565, 1, 45, 97, 105, 25, 177, 1, 401, 156, 47
Offset: 1

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Author

Antti Karttunen, Aug 05 2020

Keywords

Comments

Even terms occur on square n, odd terms on nonsquare n.
Numbers k such that a(k) = 2^e for e >= 1, are: 4, 25, 841, 12769, 66896041, etc., i.e., terms of A073715 squared.

Links

Crossrefs

Cf. A000203, A001065, A003961, A003973, A073715, A252748, A286385, A326042, A336852.
Cf. A336850 [= gcd(a(n),A003961(n))].

Programs

  • PARI
    A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A336851(n) = (sigma(A003961(n)) - A003961(n));

Formula

a(n) = A003973(n) - A003961(n) = A000203(A003961(n)) - A003961(n).
a(n) = A001065(A003961(n)).
a(n) = A336852(n) - A286385(n).

Extensions

Comments edited by Antti Karttunen, Jul 03 2023

A074626 Prime following the n-th Mersenne prime.

Original entry on oeis.org

5, 11, 37, 131, 8209, 131101, 524309, 2147483659, 2305843009213693967, 618970019642690137449562141, 162259276829213363391578010288167, 170141183460469231731687303715884105757
Offset: 1

Views

Author

Labos Elemer, Aug 26 2002

Keywords

Links

Crossrefs

Cf. A000668, A073715, A151800, A365160.

Programs

  • Maple
    a:= n-> nextprime(numtheory[mersenne]([n])):
seq(a(n), n=1..12);  # Alois P. Heinz, Oct 30 2024
  • Mathematica
    Table[NextPrime[2^MersennePrimeExponent[n] - 1], {n, 1, 12}] (* Amiram Eldar, Aug 10 2024 *)

Formula

a(n) = prime(primepi(A000668(n))+1).
From Amiram Eldar, Aug 10 2024: (Start)
a(n) = A151800(A000668(n)).
a(n) = A000668(n) + A365160(n). (End)

A365161 Least k such that A000668(n) - k is prime, where A000668(n) is the n-th Mersenne prime.

Original entry on oeis.org

1, 2, 2, 14, 12, 8, 18, 18, 30, 20, 170, 24, 114, 56, 156, 2510, 1824, 12, 3980, 3630, 16902, 284, 7712, 20022, 12930, 9698, 16232, 1058, 256016, 23712, 26298
Offset: 1

Views

Author

Robert P. P. McKone, Aug 24 2023

Keywords

Comments

The distance between the n-th Mersenne prime and the previous prime.

Examples

			A000668(6) = 131071, the previous prime is 131063, so a(6) = 131071 - 131063 = 8.

Crossrefs

Cf. A000040, A000668 (Mersenne primes), A001223, A059305, A073715, A365160.

Programs

  • Mathematica
    m[n_] := m[n] = (2^MersennePrimeExponent[n] - 1); a[k_, n_] := a[k, n] = m[n] - k; l[k_, n_] := l[k, n] = PrimeQ[a[k, n]]; Table[k = 1; Monitor[Parallelize[While[True, If[l[k, n], Break[]]; k++]; k], {n, k}], {n, 1, 20}]

Formula

a(n) = A001223(A059305(n)-1). - Michel Marcus, Aug 25 2023
a(n) = A000668(n) - A073715(n). - Amiram Eldar, Aug 10 2024

Extensions

a(29)-a(31) from Michael S. Branicky, Sep 01 2024
Showing 1-3 of 3 results.

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

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