A383296 Primorial base echo numbers: primorial base expansion of k has the largest prime factor of k-1 as its suffix.

11, 41, 59, 101, 127, 137, 161, 221, 229, 251, 313, 323, 337, 401, 551, 641, 667, 703, 757, 799, 881, 929, 1001, 1013, 1093, 1157, 1177, 1211, 1369, 1541, 1583, 1601, 1667, 1753, 1873, 1939, 2017, 2177, 2201, 2393, 2501, 2509, 2561, 2647, 2669, 3043, 3079, 3197, 3217, 3433, 3521, 3613, 3649, 3653, 3823, 3851, 4001

Offset

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences related to primorial base.

Example

The first seven terms:
    k     A049345(k)  A006530(k-1) (in primorial base)
   11  =        121         5        (21)
   41  =       1121         5        (21)
   59  =       1421        29        (421)
  101  =       3121         5        (21)
  127  =       4101         7        (101)
  137  =       4221        17        (221)
  161  =       5121         5        (21).

Prog

(PARI)
A006530(n) = if(1==n, n, my(f=factor(n)); f[#f~, 1]);
isA383296(n) =  if(n<2, 0, my(p=2, k=A006530(n-1)); while(k, if((k%p)!=(n%p), return(0)); n = n\p; k = k\p; p = nextprime(1+p)); (1));

Crossrefs

Primorial base (A049345) analog of A383896.

Subsequence of A383297.

Cf. A006530.

Sequence in context: A370156 A122015 A192820 * A078653 A389477 A040167

Adjacent sequences: A383293 A383294 A383295 * A383297 A383298 A383299

Keyword

nonn,base

Author

Antti Karttunen, May 15 2025

Status

approved