Search: id:A119892
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%I A119892
%S A119892 2999,3989,4799,4889,5879,5897,5987,6599,6689,6779,6869,6959,6977,7499,
%T A119892 7589,7877,7949,8597,8669,8849,8867,9479,9497,9587,9677,9749,9767,9839,
%U A119892 9857,9929,12899,13799,13997,14699,14879,14897,14969,15797,15887,15959
%N A119892 Prime quartet leaders : largest number of a prime quartet.
%C A119892 A prime quartet is a set of four different prime numbers such that the 
               fourth number is a 1-digit number which is the sum of the digits 
               of the third number, the third number is the sum of the digits of 
               the second number and the second number is the sum of the digits 
               of the first number.
%C A119892 Different from A106766.
%C A119892 Comment from Joshua Zucker (joshua.zucker(AT)gmail.com), Apr 24 2007, 
               on the difference between this sequence and A106766: The digit sum 
               must be the largest member of a prime trio, so the first number where 
               the sequences differ must be with digit sum 47 and thus have at least 
               6 digits - so until then you get all the primes with 4 or 5 digits 
               that have digit sum 29.
%C A119892 a(2322)=389999 is the first value different from A106766, where A106766(2322)=390359. 
               See also A106778 = primes with digit sum = 47: A106778(1)=389999. 
               - Martin Fuller (martin_n_fuller(AT)btinternet.com) and Ray Chandler 
               (rayjchandler(AT)sbcglobal.net), Apr 24 2007
%H A119892 L. Stevens, <a href="http://www.lucstevens.com/Primeensembles.htm">Prime 
               ensembles</a>
%e A119892 2999 is in the sequence because it is the largest number of the prime 
               quartet (2999,29,11,2)
%o A119892 (PARI code from Martin Fuller) DigitSum(n,b=10)=local(x);x=0;while(n,
               x+=n%b;n\=b);x
%o A119892 PrimeEnsemble(n,b=10)=local(x);x=1;while(ispseudoprime(n),if(n<b,return(x));
               n=DigitSum(n,b);x++);0
%o A119892 forprime(p=2, 16000, if(PrimeEnsemble(p)>=4, print1(p", ")));
%Y A119892 Cf. A119889, A119890, A119891.
%Y A119892 Sequence in context: A063055 A031130 A106766 this_sequence A158861 A156655 
               A128935
%Y A119892 Adjacent sequences: A119889 A119890 A119891 this_sequence A119893 A119894 
               A119895
%K A119892 base,nonn
%O A119892 1,1
%A A119892 Luc Stevens (lms022(AT)yahoo.com), May 27 2006

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