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Prime duet leaders: largest number of a prime duet.
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%I #16 Nov 01 2024 20:47:36

%S 11,23,41,43,61,101,113,131,151,223,241,311,313,331,401,421,601,1013,

%T 1031,1033,1051,1103,1123,1213,1231,1301,1303,1321,2003,2111,2113,

%U 2131,2203,2221,2311,3011,3121,3301,4001,4003,4021,4111,4201,5011,5101,10103

%N Prime duet leaders: largest number of a prime duet.

%C A prime duet is a pair of two different prime numbers such that the second number is a 1-digit number which is the sum of the digits of the first number.

%C The terms of the sequence must be at least 2 digits in length, so {5,5} is not a prime duet. - _Harvey P. Dale_, May 07 2021

%H David A. Corneth, <a href="/A119890/b119890.txt">Table of n, a(n) for n = 1..10000</a> (first 600 terms from Harvey P. Dale)

%H L. Stevens, <a href="http://www.lucstevens.com/Primeensembles.htm">Prime ensembles</a>

%H David A. Corneth, <a href="/A119890/a119890.gp.txt">PARI program</a>

%e 113 is in the sequence because it is the largest number of the prime duet (113,5)

%t Select[Prime[Range[5,1300]],IntegerLength[Total[IntegerDigits[#]]]==1&&PrimeQ[Total[IntegerDigits[#]]]&] (* _Harvey P. Dale_, May 07 2021 *)

%o (PARI) \\ See PARI link. _David A. Corneth_, May 07 2021

%Y Cf. A119889, A119891, A119892.

%K nonn,base

%O 1,1

%A Luc Stevens (lms022(AT)yahoo.com), May 27 2006

%E Corrected by _Harvey P. Dale_, May 07 2021