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A320869
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Primes such that p + digitsum(p, base 16) is again a prime.
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1
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17, 19, 23, 29, 31, 53, 59, 89, 127, 149, 151, 157, 179, 181, 211, 223, 241, 251, 263, 269, 331, 359, 367, 397, 419, 431, 449, 457, 461, 463, 487, 541, 563, 571, 593, 599, 601, 631, 659, 661, 701, 733, 761, 769, 809, 811, 839, 907, 911, 941, 971, 997, 1049, 1087, 1109, 1171, 1201, 1237, 1283, 1289, 1291
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OFFSET
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1,1
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COMMENTS
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Such primes exist only for an even base b. See A048519, A243441, A320866, A320867 and A320868 for the analog in base 10, 2, 4, 6 and 8, respectively. Also, as in base 10, there are no such primes when + is changed to -, see comment in A243442.
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LINKS
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EXAMPLE
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17 = 16 + 1 = 11[16] (in base 16), and 17 + 1 + 1 = 19 is again prime.
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MAPLE
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digsum:= (n, b) -> convert(convert(n, base, b), `+`):
select(p -> isprime(p) and isprime(p+digsum(p, 16)), [2, seq(i, i=3..1000, 2)]); # Robert Israel, Nov 07 2018
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PROG
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(PARI) forprime(p=1, 1999, isprime(p+sumdigits(p, 16))&&print1(p", "))
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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