A251360 Numbers k such that k is the concatenation of prime factors of pi(k), in increasing order.

1117, 2163, 2537, 5137, 222926801

Offset: 1

Author

Jahangeer Kholdi, Dec 01 2014

Keywords

• nonn
• base
• more

Comments

Numbers k such that k = A037276(A000720(k)).

Conjecture: numbers k such that k = A084317(A000720(k)). - Chai Wah Wu, Apr 04 2018

a(6) > 10^12 if exists. - Max Alekseyev, May 16 2025

Examples

			1117 is in the sequence since pi(1117) = 11*17,
2163 is in the sequence since pi(2163) = 2*163,
2537 is in the sequence since pi(2537) = 2*5*37,
and 5137 is in the sequence since pi(5137) = 5*137.
		

Links

• Chris Caldwell, G. L. Honaker and Lewis, 1117

Crossrefs

Cf. A000040, A000720, A251361, A251362.

Programs

Mathematica

a251360[n_Integer] := Select[Range[n], # == FromDigits[Flatten@IntegerDigits[First@ Transpose@ FactorInteger[PrimePi[#]]]] &]; a251360[10^5] (* Michael De Vlieger, Dec 03 2014 *)

Python

from sympy import prime, factorint
A251360_list, p = [], 3
for n in range(2,10**6):
    q, fn = prime(n+1), factorint(n)
    m = int(''.join(str(d)*fn[d] for d in sorted(fn)))
    if p <= m < q:
        A251360_list.append(m)
    p = q # Chai Wah Wu, Dec 10 2014, corrected Apr 04 2018

Extensions

a(5) from Chai Wah Wu, Dec 10 2014