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A343139 Numbers k that satisfy the condition digitsum(k) = digitsum(pi(k)) where pi is the prime counting function. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

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

LINKS

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

EXAMPLE

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.

MATHEMATICA

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

PROG

(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

CROSSREFS

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

Sequence in context: A110978 A274433 A227804 * A087719 A174216 A249874

Adjacent sequences:  A343136 A343137 A343138 * A343141 A343142 A343144

KEYWORD

nonn,easy,base

AUTHOR

K. D. Bajpai, Apr 06 2021

STATUS

approved

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Last modified June 14 15:36 EDT 2021. Contains 345025 sequences. (Running on oeis4.)