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.

A223548 Smallest prime factors for sequence A223546.

Original entry on oeis.org

13, 229, 269, 331, 1036991, 193, 1187, 379, 942381313, 1078717, 1690920279179, 593, 181, 1433, 641, 139, 631, 2622013, 1123, 130337, 223, 155784593, 3746107, 1223, 13791824242727551, 67623587, 853, 299635177, 3966293, 197, 4755811387725362803, 263, 40637, 577
Offset: 1

Views

Author

Paul Larm, Mar 21 2013

Keywords

Examples

			a(3) = 229, the smallest prime factor of A223546(3) = 233335657 = 229*307*3319.

Links

Crossrefs

Cf. A020639, A223546, A285528.

Formula

a(n) = A020639(A223546(n)).
a(n) = 463 for n >= 74. - Sean A. Irvine, Jul 20 2025

Extensions

a(15)-a(34) from Chai Wah Wu, Oct 10 2019

A217723 a(n) = (sum of first n primorial numbers) minus 1.

Original entry on oeis.org

1, 7, 37, 247, 2557, 32587, 543097, 10242787, 233335657, 6703028887, 207263519017, 7628001653827, 311878265181037, 13394639596851067, 628284422185342477, 33217442899375387207, 1955977793053588026277, 119244359152460559009547
Offset: 1

Views

Author

Paul Larm, Mar 21 2013

Keywords

Examples

			For n = 4, a(4) = 2 + 2*3 + 2*3*5 + 2*3*5*7 - 1 = 247.

Links

Crossrefs

Equals A060389 - 1. Cf. A223546, A223548.

Programs

  • Mathematica
    Accumulate[Denominator[Accumulate[1/Prime[Range[20]]]]] - 1 (* Alonso del Arte, Mar 21 2013 *)
Accumulate[Table[Fold[Times,Prime[Range[n]]],{n,20}]]-1 (* Harvey P. Dale, May 23 2020 *)

Formula

a(1) = P(1)# - 1, a(2) = P(1)# + P(2)# -1; where P(n)# is the product of first n prime numbers (primorial#).

A285528 Numbers n such that A217723(n) (sum of first n primorial numbers minus 1) is prime.

Original entry on oeis.org

2, 3, 5, 6, 7, 8, 11, 14, 21, 41, 42, 43, 74, 78
Offset: 1

Views

Author

Amiram Eldar, Apr 20 2017

Keywords

Comments

This sequence is finite since 463 (the 90th prime) divides A217723(89) and thus all the succeeding terms of A217723 are also divisible by 463.
The associated primes are: 7, 37, 2557, 32587, 543097, 10242787, 207263519017, 13394639596851067, 41295598995285955839203627497, 2.998... * 10^70, 5.427... * 10^72, 1.036... * 10^75, 4.549... * 10^150 and 1.019... * 10^161. They are a subsequence of A127729.

Examples

			A217723(5) = 2 + 2*3 + 2*3*5 + 2*3*5*7 + 2*3*5*7*11 - 1 = 2557 is prime, thus 5 is in this sequence.

Crossrefs

Cf. A002110, A217723, A127729, A223546.

Programs

  • Maple
    select(m -> isprime(add(mul(ithprime(i),i=1..j),j=1..m)-1), [$1..89]); # Robert Israel, Apr 20 2017
  • Mathematica
    primorial[n_] := Product[Prime[i], {i, n}]; a[n_] := Sum[primorial[i], {i, 1, n}]-1; Select[Range[0, 100], PrimeQ[a[#]] &]
(* Second program: *)
Flatten@ Position[Accumulate@ FoldList[#1 #2 &, Prime@ Range@ 200] - 1 /. k_ /; k == 1 || CompositeQ@ k -> 0, m_ /; m != 0] (* Michael De Vlieger, Apr 23 2017 *)
Showing 1-3 of 3 results.

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

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