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A343139 Numbers k that satisfy the condition digitsum(k) = digitsum(pi(k)) where pi is the prime counting function. 1

%I

%S 15,27,51,63,120,130,131,142,153,164,208,218,230,242,252,262,263,274,

%T 305,318,327,338,348,360,370,381,392,413,424,435,446,456,457,702,712,

%U 722,732,805,860,901,912,922,932,1016,1027,1038,1039,1048,1049,1059,1071,1080

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

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

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

%H David A. Corneth, <a href="/A343139/b343139.txt">Table of n, a(n) for n = 1..10000</a>

%e 153 is a term because the number of primes up to 153 is 36 and 1 + 5 + 3 = 9 = 3 + 6.

%e 435 is a term because number of primes up to 435 is 84 and 4 + 3 + 5 = 12 = 8 + 4.

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

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

%o (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

%o (Python)

%o from sympy import primepi

%o def sd(n): return sum(map(int, str(n)))

%o def ok(n): return sd(n) == sd(primepi(n))

%o print(list(filter(ok, range(1, 1081)))) # _Michael S. Branicky_, May 28 2021

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

%K nonn,easy,base

%O 1,1

%A _K. D. Bajpai_, Apr 06 2021

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Last modified July 24 20:26 EDT 2021. Contains 346273 sequences. (Running on oeis4.)