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 1-2 of 2 results.

A179818 Primes in A179816.

Original entry on oeis.org

17, 131, 223, 97, 113, 127, 149, 181, 211, 241, 293, 307, 941, 367, 397, 419, 421, 1303, 457, 479, 487, 557, 587, 631, 1931, 661, 683, 691, 719, 727, 743, 773, 787, 797, 809, 811, 839, 863, 877, 907, 929, 937, 953, 967, 983, 1009, 1021, 1049, 1051, 1087, 1117
Offset: 0

Views

Author

Odimar Fabeny, Jul 28 2010

Keywords

Comments

From Robert G. Wilson v, Aug 02 2010: (Start)
These occur at the n-th decade: 1, 5, 8, 10, 12, 13, 15, 19, 22, 25, 30, ..., .
And sorted the sequence is 17, 97, 113, 127, 131, 149, 181, 211, 223, 241, ..., . (End)

Crossrefs

Cf. A000040, A179816.

Programs

  • Mathematica
    f[n_] := Plus @@ Select[ Range[10 n + 1, 10 n + 9], PrimeQ]; Select[f@# & /@ Range[0, 111], PrimeQ] (* Robert G. Wilson v, Aug 02 2010 *)

Extensions

More terms from Robert G. Wilson v, Aug 02 2010

A356690 Product of the prime numbers that are between 10*n and 10*(n+1).

Original entry on oeis.org

210, 46189, 667, 1147, 82861, 3127, 4087, 409457, 7387, 97, 121330189, 113, 127, 2494633, 149, 23707, 27221, 30967, 181, 1445140189, 1, 211, 11592209, 55687, 241, 64507, 70747, 75067, 79523, 293, 307, 30857731, 1, 111547, 121103, 126727, 367, 141367, 148987, 397, 164009, 419, 421
Offset: 0

Views

Author

Hemjyoti Nath, Aug 23 2022

Keywords

Comments

a(n) is prime iff n is in A216292. - Amiram Eldar, Aug 23 2022
For almost all n (in the sense of natural density), a(n) = 1. - Charles R Greathouse IV, Sep 30 2022

Examples

			210 = 2*3*5*7, 46189 = 11*13*17*19, 667 = 23*29, 1147 = 31*37, 82861 = 41*43*47.

Crossrefs

Cf. A000040, A000720, A032352, A179816, A216292.

Programs

  • Mathematica
    a[n_] := Times @@ Select[Range[10 n + 1, 10 n + 9], PrimeQ]; Array[a, 43, 0]
  • PARI
    a(n) = vecprod(select(isprime, [10*n..10*(n+1)])); \\ Michel Marcus, Aug 24 2022
  • Python
    from math import prod
from sympy import primerange
def a(n): return prod(primerange(10*n, 10*(n+1)))
print([a(n) for n in range(43)]) # Michael S. Branicky, Aug 23 2022
  • Python
    from math import prod
from sympy import isprime
def A356690(n): return prod(m for i in (1,3,7,9) if isprime(m:=10*n+i)) if n else 210 # Chai Wah Wu, Sep 23 2022

Formula

Let m(n) = {isprime(10n-9) * (10n-9), isprime(10n-8) * (10n-8), isprime(10n-7) * (10n-7), isprime(10n-5) * (10n-5), isprime(10n-3) * (10n-3), isprime(10n-1) * (10n-1)}, where isprime = A010051; then a(n) = product of nonzero terms from m(n).
a(n) = 1 for n in A032352. - Michel Marcus, Aug 23 2022
a(n) = Product_{i=1+pi(10*n)..pi(10*(n+1))} prime(i). - Alois P. Heinz, Aug 23 2022
Showing 1-2 of 2 results.

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

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