A062347 a(n) = (product of first n primes) modulo prime(n+1).

1, 2, 1, 2, 1, 9, 8, 18, 15, 17, 19, 11, 6, 26, 35, 27, 15, 55, 30, 24, 28, 4, 47, 56, 28, 28, 75, 25, 105, 30, 9, 52, 111, 89, 46, 132, 53, 97, 104, 106, 42, 94, 158, 184, 155, 5, 6, 45, 87, 78, 86, 26, 120, 33, 242, 66, 86, 2, 214, 2, 198, 127, 14, 112, 7, 141, 77, 309

Offset: 0

Author

Henry Bottomley, Jul 06 2001

Keywords

• nonn

Examples

			a(4)=1 since 2*3*5*7 = 210 = 19*11 + 1.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000 (first 1001 terms from Harry J. Smith)

Crossrefs

Cf. A000040, A002110, A051126, A102647.

Programs

Mathematica

Mod[ #[ [ 1 ] ], #[ [ 2 ] ] ]&/@ Transpose[ {FoldList[ Times, 1, Prime[ Range[ 70 ] ] ], Prime[ Range[ 71 ] ]} ]
Join[{1},Module[{nn=70,prs},prs=Prime[Range[nn]];Table[Mod[Fold[Times,Take[prs,n-1]],prs[[n]]],{n,2,nn}]]] (* Harvey P. Dale, Jun 30 2024 *)

PARI

{ n=-1; f=1; forprime (p=2, prime(1001), write("b062347.txt", n++, " ", f%p); f*=p ) } \\ Harry J. Smith, Aug 05 2009

Python

from sympy import sieve, primorial
print([1] + [primorial(k) % sieve[k+1] for k in range(1, 71)])
# Karl-Heinz Hofmann, Jan 26 2022

Formula

a(n) = A051126(A002110(n), A000040(n+1)).