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

Author

Antti Karttunen, May 15 2025

Keywords

• nonn
• base

Examples

			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).
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to primorial base.

Crossrefs

Primorial base (A049345) analog of A383896.

Subsequence of A383297.

Cf. A006530.

Programs

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));