A377877 The n-th primorial number reduced modulo 3125.

1, 2, 6, 30, 210, 2310, 1905, 1135, 2815, 2245, 2605, 2630, 435, 2210, 1280, 785, 980, 1570, 2020, 965, 2890, 1595, 1005, 2165, 2060, 2945, 570, 2460, 720, 355, 2615, 855, 2630, 935, 1840, 2285, 1285, 1745, 60, 645, 2210, 1840, 1790, 1265, 395, 2815, 810, 2160, 430, 735, 2690, 1770, 1155, 230, 1480, 2235, 305, 795

Offset: 0

Author

Antti Karttunen, Nov 13 2024

Keywords

• nonn
• less

Links

• Antti Karttunen, Table of n, a(n) for n = 0..15625
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A002110.

Cf. also A086360, A377876.

Programs

Mathematica

Mod[FoldList[Times, 1, Prime[Range[100]]], 3125] (* Paolo Xausa, Nov 13 2024 *)

PARI

A002110(n) = prod(i=1,n,prime(i));
A377877(n) = (A002110(n)%3125);

PARI

up_to = 15625;
A377877list(up_to_n) = { my(m=5^5, v=vector(1+up_to_n), pr=1); v[1] = 1; for(n=1, up_to_n, pr *= Mod(prime(n),m); v[1+n] = lift(pr)); (v); };
v377877 = A377877list(up_to);
A377877(n) = v377877[1+n];

Formula

a(n) = A002110(n) mod (5^5).