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A235146 a(n) = Least integer k such that it takes n iterations of "factor and reverse bits of odd prime divisors" (A235027) before a fixed point or cycle of 2 is reached; records in A235145.

%I A235146 #29 Aug 06 2017 22:21:20
%S A235146 0,19,139,719,4793,23773,260863,2375231,21793843
%N A235146 a(n) = Least integer k such that it takes n iterations of "factor and reverse bits of odd prime divisors" (A235027) before a fixed point or cycle of 2 is reached; records in A235145.
%C A235146 Note, as for all composite values A235145(u * v) = max(A235145(u), A235145(v)) which can be further reduced as A235145(n) = Max_{p|n} A235145(p), and because for any odd prime p, lpf(A056539(p)) >= 3 (where lpf = A020639, the least prime dividing n) while 1/2 < A056539(n)/n < 2, it follows that this sequence gives also the positions of the records in A235145, as its new values must appear in order.
%C A235146 Also, because of that multiplicativity criterion, all terms (after zero) must be primes, and specifically, the terms are a subset of A235030 (i.e., of A204219).
%C A235146 Conjecture: additional property is that the primes here belong to that subset of p in A204219 for which A056539(p) > p. The list of such primes begins as: 19, 79, 103, 137, 139, 149, 157, 179, 191, 239, 271, 281, 293, 311, 317, 347, 367, 379, 439, 523, 541, 547, 557, 563, 569, 587, 607, 613, 647, 659, 719, 733, 743, 751, 787, ...
%o A235146 (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o A235146 (define A235146 (RECORD-POS 1 0 A235145))
%o A235146 (PARI) revbits(n) = fromdigits(Vecrev(binary(n)), 2);
%o A235146 a235027(n) = {f = factor(n); for (k=1, #f~, if (f[k,1] != 2, f[k,1] = revbits(f[k,1]););); factorback(f);}
%o A235146 find(v, newn) = {for(k=1, #v, if (v[#v -k + 1] == newn, return (k));); return (0);}
%o A235146 a235145(n) = {ok = 0; v = [n]; while (! ok, newn = a235027(n); ind = find(v, newn); if (ind, ok = 1, v = concat(v, newn); n = newn);); #v - ind;}
%o A235146 a(n) = {k = 0; while (a235145(k) != n, k = nextprime(k+1)); k;}
%o A235146 lista(nn) = {kprec = 0; for (n=0, nn, k = kprec; while (a235145(k) != n, k = nextprime(k+1)); print1(k, ", "); kprec = k;);} \\ _Michel Marcus_, Aug 06 2017
%Y A235146 A subset of A235030 and A204219.
%Y A235146 Cf. A235145, A235027, A056539.
%K A235146 nonn,base,more,hard
%O A235146 0,2
%A A235146 _Antti Karttunen_, Jan 03 2014
%E A235146 a(5)-a(8) from _Michel Marcus_, Aug 06 2017