A392864 a(n) = Sum_{i=1..n} (A392614(1+n) mod prime(i))*A002110(i-1).

0, 1, 5, 11, 191, 1007, 14867, 255107, 9129053, 67327193, 4529184593, 166271515343, 4779162788333, 138352449214913, 3789355611541433, 239279059581601973, 24834870363121258373, 1393579526405103137033, 18698422677793016888663, 2129889287147118494587523, 536495754760605278294365643, 21180306469448466834088735073

Offset

0,3

Comments

By definition, the resulting primorial base expansions (see examples) never contain any zeros for n > 0, not even "hidden leading zeros", i.e., this is a subsequence of A328574 and also A267263(a(n)) == n for all n.

Links

Antti Karttunen, Table of n, a(n) for n = 0..349

Index entries for sequences related to primorial base.

Index entries for sequences related to primorial numbers.

Example

n                    a(n)                                  A049345(a(n))
---+---------------------------------------------------------------------
0  |                    0,                                            0,
1  |                    1,                                            1,
2  |                    5,                                          2:1,
3  |                   11,                                        1:2:1,
4  |                  191,                                      6:1:2:1,
5  |                 1007,                                    4:5:2:2:1,
6  |                14867,                                  6:4:5:2:2:1,
7  |               255107,                                8:6:4:5:2:2:1,
8  |              9129053,                          17:14:12:10:4:3:2:1,
9  |             67327193,                        6:17:14:12:10:4:3:2:1,
10 |           4529184593,                     20:6:17:14:12:10:4:3:2:1,
11 |         166271515343,                  25:20:6:17:14:12:10:4:3:2:1,
12 |        4779162788333,               23:25:20:6:17:14:12:10:4:3:2:1,
13 |      138352449214913,            18:23:25:20:6:17:14:12:10:4:3:2:1,
14 |     3789355611541433,         12:18:23:25:20:6:17:14:12:10:4:3:2:1,
15 |   239279059581601973,      18:12:18:23:25:20:6:17:14:12:10:4:3:2:1,
16 | 24834870363121258373,   40:18:12:18:23:25:20:6:17:14:12:10:4:3:2:1,
etc.
The digits in the primorial base expansion of the terms, from term a(8) up to term a(11980-1), when read from right to left, give the terms of sequence A392862, and at n=11980, the pattern changes again.
Compare to the pattern in A392863.

Prog

(PARI)
A002110(n) = prod(i=1, n, prime(i));
A143293(n) = { if(n==0, return(1)); my(P=1, s=1); forprime(p=2, prime(n), s+=P*=p); s; };
A392614(n) = if(!n, n, my(pr=A002110(n)); for(k=A143293(n-1), oo, if(1==gcd(k, pr), return(k))));
A392864(n) = { my(x=A392614(1+n)); sum(i=1, n, (x%prime(i))*A002110(i-1)); };

Crossrefs

Cf. A002110, A049345, A143293, A267263, A392614, A392615, A392862, A392863.

Subsequence of A328574.

Sequence in context: A179388 A336623 A229907 * A181491 A375161 A006572

Adjacent sequences: A392861 A392862 A392863 * A392865 A392866 A392867

Keyword

nonn,base

Author

Antti Karttunen, Jan 26 2026

Status

approved