A343139 Numbers k that satisfy the condition digitsum(k) = digitsum(pi(k)) where pi is the prime counting function.

15, 27, 51, 63, 120, 130, 131, 142, 153, 164, 208, 218, 230, 242, 252, 262, 263, 274, 305, 318, 327, 338, 348, 360, 370, 381, 392, 413, 424, 435, 446, 456, 457, 702, 712, 722, 732, 805, 860, 901, 912, 922, 932, 1016, 1027, 1038, 1039, 1048, 1049, 1059, 1071, 1080

Offset: 1

Author

K. D. Bajpai, Apr 06 2021

Keywords

• nonn
• easy
• base

Comments

a(7) = 131 is the first prime in this sequence.

A033548 (Honaker primes) is a subsequence of this sequence.

Examples

			153 is a term because the number of primes up to 153 is 36 and 1 + 5 + 3 = 9 = 3 + 6.
435 is a term because number of primes up to 435 is 84 and 4 + 3 + 5 = 12 = 8 + 4.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000720, A007953, A010846, A033548, A033549.

Programs

Mathematica

fHQ[n_] := Plus @@ IntegerDigits@n == Plus @@ IntegerDigits@PrimePi@n; Select[Range[3000], fHQ[#] &]

PARI

for(n=1, 5000, if(sumdigits(n)==vecsum(digits(primepi(n))), print1(n, ", " )));

PARI

upto(n) = { my(q = 2, ulim = nextprime(n), pi = 0, res = List()); forprime(p = 3, ulim, pi++; for(i = q, p-1, if(sumdigits(i) == sumdigits(pi), listput(res, i) ) ); q = p ); res } \\ David A. Corneth, May 26 2021

Python

from sympy import primepi
def sd(n): return sum(map(int, str(n)))
def ok(n): return sd(n) == sd(primepi(n))
print(list(filter(ok, range(1, 1081)))) # Michael S. Branicky, May 28 2021