1,1

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.

Different from A106766.

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.

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

L. Stevens, Prime ensembles

2999 is in the sequence because it is the largest number of the prime quartet (2999,29,11,2)

(PARI code from Martin Fuller) DigitSum(n, b=10)=local(x); x=0; while(n, x+=n%b; n\=b); x

PrimeEnsemble(n, b=10)=local(x); x=1; while(ispseudoprime(n), if(n<b, return(x)); n=DigitSum(n, b); x++); 0

forprime(p=2, 16000, if(PrimeEnsemble(p)>=4, print1(p", ")));

Cf. A119889, A119890, A119891.

Sequence in context: A063055 A031130 A106766 this_sequence A158861 A156655 A128935

Adjacent sequences: A119889 A119890 A119891 this_sequence A119893 A119894 A119895

base,nonn

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