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A188366 Values of c such that (c+9*b)*Prime(n)#-1 is the least prime such that (c+k*b)*Prime(n)#-1 is prime for k=0 to 9 with c+9*b < Prime(n)# , or 0 if no solution. Prime(n)#=n-th primorial 2

%I #23 Jun 04 2022 21:50:32

%S 0,0,0,0,0,653,1542,2035,2460,7473,654,7394,7479,69698,4646,25205,

%T 122774,42953,444644,38761,545933,83675,212892,87123,106714,50427,

%U 747235,1737780,2371271,1807313

%N Values of c such that (c+9*b)*Prime(n)#-1 is the least prime such that (c+k*b)*Prime(n)#-1 is prime for k=0 to 9 with c+9*b < Prime(n)# , or 0 if no solution. Prime(n)#=n-th primorial

%C b=A188367(n), c*Prime(n)#-1 is the first of an arithmetic progression of 10 primes or more.

%C I use PFGW program from primeform group to generate the primes and my own sieve to find the least sum c+9*b for an arithmetic progression of at least 10 primes, all primes are certified primes by PFGW program.

%e 13#=30030, 30030*653-1=19609589 , 289*30030=8678670

%e 196095899+k*8678670 is prime for k=0 to 9 for n=6 c=653

%e and b=289

%Y Cf. A188367.

%K nonn,hard

%O 1,6

%A _Pierre CAMI_, Mar 29 2011

%E More terms from Pierre CAMI

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Last modified April 25 04:42 EDT 2024. Contains 371964 sequences. (Running on oeis4.)