A251360 - OEIS

%I #41 Apr 15 2018 13:53:32

%S 1117,2163,2537,5137,222926801

%N Numbers n such that n is the concatenation of prime factors of pi(n), in increasing order.

%C Next term must be greater than 2*10^7.

%C Numbers n such that n = A037276(A000720(n)).

%C a(6) > 4.5*10^9. - _Chai Wah Wu_, Dec 11 2014

%C Conjecture: a(n) are numbers n such that n = A084317(A000720(n)). - _Chai Wah Wu_, Apr 04 2018

%H Chris Caldwell, G. L. Honaker and Lewis, <a href="https://primes.utm.edu/curios/page.php/1117.html">1117</a>

%e 1117 is in the sequence since pi(1117) = 11*17,

%e 2163 is in the sequence since pi(2163) = 2*163,

%e 2537 is in the sequence since pi(2537) = 2*5*37,

%e and 5137 is in the sequence since pi(5137) = 5*137.

%t a251360[n_Integer] := Select[Range[n], # ==

%t FromDigits[Flatten@IntegerDigits[First@ Transpose@ FactorInteger[PrimePi[#]]]] &]; a251360[10^5] (* _Michael De Vlieger_, Dec 03 2014 *)

%o (Python)

%o from sympy import prime, factorint

%o A251360_list, p = [], 3

%o for n in range(2,10**6):

%o ....q, fn = prime(n+1), factorint(n)

%o ....m = int(''.join(str(d)*fn[d] for d in sorted(fn)))

%o ....if p <= m < q:

%o ........A251360_list.append(m)

%o ....p = q # _Chai Wah Wu_, Dec 10 2014, corrected Apr 04 2018

%Y Cf. A000040, A000720, A251361, A251362.

%K nonn,base,more

%O 1,1

%A _Jahangeer Kholdi_, Dec 01 2014

%E a(5) from _Chai Wah Wu_, Dec 10 2014