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A343139
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Numbers k that satisfy the condition digitsum(k) = digitsum(pi(k)) where pi is the prime counting function.
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1
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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
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OFFSET
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1,1
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COMMENTS
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a(7) = 131 is the first prime in this sequence.
A033548 (Honaker primes) is a subsequence of this sequence.
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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fHQ[n_] := Plus @@ IntegerDigits@n == Plus @@ IntegerDigits@PrimePi@n; Select[Range[3000], fHQ[#] &]
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PROG
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(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))
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CROSSREFS
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KEYWORD
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nonn,easy,base
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AUTHOR
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STATUS
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approved
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