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

%I A383296 #8 May 15 2025 08:18:44
%S A383296 11,41,59,101,127,137,161,221,229,251,313,323,337,401,551,641,667,703,
%T A383296 757,799,881,929,1001,1013,1093,1157,1177,1211,1369,1541,1583,1601,
%U A383296 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
%N A383296 Primorial base echo numbers: primorial base expansion of k has the largest prime factor of k-1 as its suffix.
%H A383296 Antti Karttunen, <a href="/A383296/b383296.txt">Table of n, a(n) for n = 1..10000</a>
%H A383296 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>.
%e A383296 The first seven terms:
%e A383296     k     A049345(k)  A006530(k-1) (in primorial base)
%e A383296    11  =        121         5        (21)
%e A383296    41  =       1121         5        (21)
%e A383296    59  =       1421        29        (421)
%e A383296   101  =       3121         5        (21)
%e A383296   127  =       4101         7        (101)
%e A383296   137  =       4221        17        (221)
%e A383296   161  =       5121         5        (21).
%o A383296 (PARI)
%o A383296 A006530(n) = if(1==n, n, my(f=factor(n)); f[#f~, 1]);
%o A383296 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));
%Y A383296 Primorial base (A049345) analog of A383896.
%Y A383296 Subsequence of A383297.
%Y A383296 Cf. A006530.
%K A383296 nonn,base
%O A383296 1,1
%A A383296 _Antti Karttunen_, May 15 2025