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Numbers n with property that the sum of n and the digital root of n is prime.
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%I #27 Sep 08 2022 08:46:10

%S 1,10,11,13,14,16,28,29,32,34,35,46,49,52,53,65,67,68,71,82,85,89,100,

%T 101,103,104,106,122,124,136,137,142,143,155,158,160,172,175,176,190,

%U 191,193,194,209,215,226,227,229,232,233,247,250,262,265,266,269,280

%N Numbers n with property that the sum of n and the digital root of n is prime.

%C Indices of primes in A064806. - _Tom Edgar_, Jan 07 2015

%C For any prime p >= 11, if p == k mod 9 then n = p - k/2 (if k is even) or p - (k+9)/2 (if k is odd) is in the sequence. - _Robert Israel_, Jan 07 2015

%p map(p -> p - (p/2 mod 9), [2, seq(ithprime(i), i=5..100)]); # _Robert Israel_, Jan 07 2015

%t Select[Range[100],PrimeQ[#+Mod[#,9]]&] (* _Ivan N. Ianakiev_, Feb 01 2015 *)

%o (Sage) [n for n in [1..200] if is_prime(n+(1+(n-1)%9))] # _Tom Edgar_, Jan 05 2015

%o (Magma) [n: n in [1..300]| IsPrime(n+(1+(n-1)mod 9))]; // _Vincenzo Librandi_, Jan 15 2015

%Y Cf. A010888, A064806.

%K nonn,base

%O 1,2

%A _Robert Gelhar_, Jan 05 2015