%I #34 Sep 26 2016 22:09:14

%S 11,13,17,19,31,23,37,29,41,43,47,59,61,53,67,79,71,73,97,89,101,83,

%T 107,109,131,103,127,139,151,113,137,149,181,163,157,179,191,173,167,

%U 199,211,193,197,229,241,223,227,239,251,233,257,269

%N Array read by rows with four columns T(n,k) in which row n lists the primes > 10 ending in 1, 3, 7, 9 respectively and not yet present in the sequence.

%H Charles R Greathouse IV, <a href="/A275467/b275467.txt">Table of n, a(n) for n = 1..10000</a>

%H A. Granville and G. Martin, <a href="http://www.jstor.org/stable/27641834">Prime number races</a>, Amer. Math. Monthly, 113 (No. 1, 2006), 1-33.

%H J. Kaczorowski, <a href="http://dx.doi.org/10.1006/jnth.1995.1006">On the Shanks-Rényi Race Problem mod 5</a>, J. Number Theory 50 (1995), 106-118.

%F From _Charles R Greathouse IV_, Jul 29 2016: (Start)

%F For n > 4, a(n) is the smallest prime greater than a(n-4) and congruent to a(n-4) mod 10.

%F a(n) ~ n log n. (End)

%F From _Omar E. Pol_, Jul 29 2016: (Start)

%F T(n,1) = A030430(n).

%F T(n,2) = A030431(n+1).

%F T(n,3) = A030432(n+1).

%F T(n,4) = A030433(n).

%F (End)

%e From _Omar E. Pol_, Jul 29 2016: (Start)

%e Array begins:

%e 11, 13, 17, 19;

%e 31, 23, 37, 29;

%e 41, 43, 47, 59;

%e 61, 53, 67, 79;

%e 71, 73, 97, 89;

%e 101, 83, 107, 109;

%e 131, 103, 127, 139;

%e 151, 113, 137, 149;

%e 181, 163, 157, 179;

%e ... (End)

%p N:= 100: # to get the first 4*N terms

%p A:= Vector(4*N);

%p for j from 1 to 4 do

%p m:= 0;

%p for k from 1 while m < N do

%p if isprime(10*k+[1,3,7,9][j]) then

%p m:= m+1; A[(m-1)*4+j]:= 10*k+[1,3,7,9][j];

%p fi

%p od

%p od:

%p convert(A,list); # _Robert Israel_, Sep 02 2016

%o (PARI) {

%o n1=10;n3=12;n7=16;n9=18;

%o for(i=1,20,

%o while(n1%10<>1,n1=nextprime(n1+1));print1(n1", ");

%o while(n3%10<>3,n3=nextprime(n3+1));print1(n3", ");

%o while(n7%10<>7,n7=nextprime(n7+1));print1(n7", ");

%o while(n9%10<>9,n9=nextprime(n9+1));print1(n9", ");

%o n1++;n3++;n7++;n9++;

%o )

%o }

%o (PARI) my(v=[1,3,7,9]); for(i=1,20, for(j=1,4, while(!isprime(v[j]+=10),); print1(v[j]", "))) \\ _Charles R Greathouse IV_, Jul 29 2016

%Y Cf. A030430, A030431, A030432, A030433.

%K nonn,base,tabf

%O 1,1

%A _Dimitris Valianatos_, Jul 28 2016

%E Better definition from _Omar E. Pol_, Jul 29 2016