A103857 -id:A103857 - cp's OEIS frontend

A103855 a(n) = prime(n)! - prime(n)# + 1.

1, 1, 91, 4831, 39914491, 6226990771, 355687427585491, 121645100399132311, 25852016738884753547131, 8841761993739701954537146306771, 8222838654177922817725362319509871, 13763753091226345046315979581573481661865191, 33452526613163807108170062053440751360901736472791

Offset: 1

Reinhard Zumkeller, Feb 20 2005

nonn

G. C. Greubel, Table of n, a(n) for n = 1..86
Reinhard Zumkeller, p(n)! - p(n)# + 1.

Cf. A103856, A103857, A103858, A103859, A103860, A103861, A103890.

Cf. A002110, A039716, A092435.

primorial[n_] := Product[Prime[i], {i, n}]; A103855[n_] := Prime[n]! - primorial[n] + 1; Array[A103855, 20] (* G. C. Greubel, May 09 2017 *)
With[{nn=15},#[[1]]-#[[2]]+1&/@Thread[{Prime[Range[nn]]!,FoldList[Times,Prime[Range[nn]]]}]] (* Harvey P. Dale, Aug 11 2025 *)

a(n) = A039716(n) - A002110(n) + 1 = A002110(n) * (A092435(n) - 1) + 1.

A103856 Smallest prime factor of prime(n)! - prime(n)# + 1.

Original entry on oeis.org

1, 1, 7, 4831, 3673, 16349, 5240507, 4159, 83, 3911, 401, 61, 66935021479, 199, 73, 152249, 379, 5014363, 181, 191, 277, 155893, 35851, 431, 1499

Offset: 1

Reinhard Zumkeller, Feb 20 2005

nonn

a(26) has 160 digits and is too large to be included here.

Amiram Eldar, Table of n, a(n) for n = 1..26
Reinhard Zumkeller, p(n)! - p(n)# + 1.

Cf. A020639, A103855, A103857, A103891.

a(n) = if(n>2, factor(prime(n)!-factorback(primes(n))+1)[1, 1], 1); \\ Jinyuan Wang, Dec 30 2024

a(n) = A020639(A103855(n)).

A103892 Greatest prime factor of prime(n)! / prime(n)# + 1.

Original entry on oeis.org

2, 2, 5, 5, 1571, 2693, 15427, 27749, 4154449757, 151585363459003, 73899633146196133, 24770877398207, 1429176066859677377, 7748318379505746557, 21662673895172922098651, 447620901583917369406703727865417431168683, 26823894708473887265117477378744683922119

Offset: 1

Reinhard Zumkeller, Feb 20 2005

nonn

Amiram Eldar, Table of n, a(n) for n = 1..30
Reinhard Zumkeller, prime(n)! / prime(n)# + 1.

Cf. A006530, A103857, A103890, A103891.

a(n) = A006530(A103890(n)).

cp's OEIS Frontend

A103855 a(n) = prime(n)! - prime(n)# + 1.

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A103856 Smallest prime factor of prime(n)! - prime(n)# + 1.

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A103892 Greatest prime factor of prime(n)! / prime(n)# + 1.

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