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%I #23 Feb 16 2021 00:59:56
%S 7,29,47,61,83,137,139,151,173,191,193,227,229,263,281,283,317,337,
%T 353,373,409,461,463,557,577,599,601,641,643,733,757,797,821,823,887,
%U 911,977,1019,1039,1051,1091,1093,1109,1129,1163,1181,1217,1237,1291
%N Primes p such that the sum of the digits is prime and the sum of the digits of 2p is also prime.
%C Note that 137 and 139 are twin primes.
%C A049084(A007953(a(n)))*A049084(A007953(2*a(n))) > 0. - _Reinhard Zumkeller_, Jun 26 2003
%H Robert Israel, <a href="/A084201/b084201.txt">Table of n, a(n) for n = 1..10000</a>
%e 2+9=11=prime for 29 and 5+8=13=prime for 58=2*29;
%e 1+3+7=11=prime for 137 and 2+7+4=13=prime for 274=2*137;
%e 1+3+9=13=prime for 139 and 2+7+8=17=prime for 278=2*139.
%p filter:= proc(n)
%p isprime(n) and isprime(convert(convert(n,base,10),`+`)) and isprime(convert(convert(2*n,base,10),`+`))
%p end proc:
%p select(filter, [seq(i,i=3..5000,2)]); # _Robert Israel_, Sep 04 2019
%t Select[Prime[Range[300]],And@@PrimeQ[Total/@{IntegerDigits[#], IntegerDigits[2 #]}]&] (* _Harvey P. Dale_, Jun 26 2011 *)
%Y Subset of A084194/2.
%Y Cf. A007953, A049084.
%K base,nonn
%O 1,1
%A _Patrick Capelle_, Jun 20 2003
%E More terms from _Reinhard Zumkeller_, Jun 26 2003
%E Offset changed to 1 by _Robert Israel_, Sep 04 2019
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