

A119892


Prime quartet leaders: largest number of a prime quartet.


5



2999, 3989, 4799, 4889, 5879, 5897, 5987, 6599, 6689, 6779, 6869, 6959, 6977, 7499, 7589, 7877, 7949, 8597, 8669, 8849, 8867, 9479, 9497, 9587, 9677, 9749, 9767, 9839, 9857, 9929, 12899, 13799, 13997, 14699, 14879, 14897, 14969, 15797, 15887, 15959
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OFFSET

1,1


COMMENTS

A prime quartet is a set of four different prime numbers such that the fourth number is a 1digit 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, 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 and Ray Chandler, Apr 24 2007


LINKS

Table of n, a(n) for n=1..40.
L. Stevens, Prime ensembles


EXAMPLE

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


PROG

(PARI) 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", "))); \\ Martin Fuller


CROSSREFS

Cf. A119889, A119890, A119891.
Sequence in context: A235754 A235529 A106766 * A158861 A329169 A236982
Adjacent sequences: A119889 A119890 A119891 * A119893 A119894 A119895


KEYWORD

base,nonn


AUTHOR

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


STATUS

approved



