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A119450
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Primes with odd digit sum.
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8
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3, 5, 7, 23, 29, 41, 43, 47, 61, 67, 83, 89, 113, 131, 137, 139, 151, 157, 173, 179, 191, 193, 197, 199, 223, 227, 229, 241, 263, 269, 281, 283, 311, 313, 317, 331, 337, 353, 359, 373, 379, 397, 401, 409, 421, 443, 449, 461, 463, 467, 487, 557, 571, 577, 593
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OFFSET
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1,1
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COMMENTS
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On average, there are as many prime numbers for which the sum of decimal digits is even as prime numbers for which it is odd [A119450]. This hypothesis, first made in 1968, has recently been proved by researchers from the Institut de Mathematiques de Luminy.
Also primes such that absolute value of difference between largest digit and the sum of all the other digits is an odd integer. This is in accordance with hypothesis of Alexandre Gelfond, proved by C. Mauduit and J. Rivat as stated in Links section. - Osama Abuajamieh, Feb 10 2017
Considering the sequence digit sums, when prime, new maximum digit sums encounter the prime numbers themselves in order. This of course implies that, for any largest considered prime Pmax in this sequence, there will exist a larger entry P2 with digit sum = Pmax. Note the data available for such scrutiny grows very slowly - considering primes through 10^12 only attains digit sum to (prime) 97. Additionally, a parallel observation can be drawn about the behavior of companion sequence A119449. Also, this sequence appears to be a subset of A156756. - Bill McEachen, Mar 26 2017
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LINKS
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FORMULA
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MAPLE
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select(t -> isprime(t) and convert(convert(t, base, 10), `+`)::odd, [seq(i, i=3..1000, 2)]); # Robert Israel, Feb 13 2017
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MATHEMATICA
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Select[Prime@ Range@ 108, OddQ@ Total@ IntegerDigits@ # &] (* Michael De Vlieger, Feb 11 2017 *)
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PROG
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CROSSREFS
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Primes with even digit sum A119449.
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KEYWORD
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base,nonn
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AUTHOR
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STATUS
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approved
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