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A084201 Primes p such that the sum of the digits is prime and the sum of the digits of 2p is also prime.

%I A084201 #25 Jan 27 2025 19:00:53
%S A084201 7,29,47,61,83,137,139,151,173,191,193,227,229,263,281,283,317,337,
%T A084201 353,373,409,461,463,557,577,599,601,641,643,733,757,797,821,823,887,
%U A084201 911,977,1019,1039,1051,1091,1093,1109,1129,1163,1181,1217,1237,1291
%N A084201 Primes p such that the sum of the digits is prime and the sum of the digits of 2p is also prime.
%C A084201 Note that 137 and 139 are twin primes.
%C A084201 A049084(A007953(a(n)))*A049084(A007953(2*a(n))) > 0. - _Reinhard Zumkeller_, Jun 26 2003
%H A084201 Robert Israel, <a href="/A084201/b084201.txt">Table of n, a(n) for n = 1..10000</a>
%e A084201 2+9=11=prime for 29 and 5+8=13=prime for 58=2*29;
%e A084201 1+3+7=11=prime for 137 and 2+7+4=13=prime for 274=2*137;
%e A084201 1+3+9=13=prime for 139 and 2+7+8=17=prime for 278=2*139.
%p A084201 filter:= proc(n)
%p A084201   isprime(n) and isprime(convert(convert(n,base,10),`+`)) and isprime(convert(convert(2*n,base,10),`+`))
%p A084201 end proc:
%p A084201 select(filter, [seq(i,i=3..5000,2)]); # _Robert Israel_, Sep 04 2019
%t A084201 Select[Prime[Range[300]],And@@PrimeQ[Total/@{IntegerDigits[#], IntegerDigits[2 #]}]&] (* _Harvey P. Dale_, Jun 26 2011 *)
%t A084201 Select[Prime[Range[500]],AllTrue[{Total[IntegerDigits[#]],Total[IntegerDigits[2#]]},PrimeQ]&] (* _Harvey P. Dale_, Jan 27 2025 *)
%Y A084201 Subset of A084194/2.
%Y A084201 Cf. A007953, A049084.
%K A084201 base,nonn
%O A084201 1,1
%A A084201 _Patrick Capelle_, Jun 20 2003
%E A084201 More terms from _Reinhard Zumkeller_, Jun 26 2003
%E A084201 Offset changed to 1 by _Robert Israel_, Sep 04 2019