A275467 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.

11, 13, 17, 19, 31, 23, 37, 29, 41, 43, 47, 59, 61, 53, 67, 79, 71, 73, 97, 89, 101, 83, 107, 109, 131, 103, 127, 139, 151, 113, 137, 149, 181, 163, 157, 179, 191, 173, 167, 199, 211, 193, 197, 229, 241, 223, 227, 239, 251, 233, 257, 269

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

A. Granville and G. Martin, Prime number races, Amer. Math. Monthly, 113 (No. 1, 2006), 1-33.

J. Kaczorowski, On the Shanks-Rényi Race Problem mod 5, J. Number Theory 50 (1995), 106-118.

Formula

From Charles R Greathouse IV, Jul 29 2016: (Start)

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

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

From Omar E. Pol, Jul 29 2016: (Start)

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

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

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

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

(End)

Example

From Omar E. Pol, Jul 29 2016: (Start)
Array begins:
11,   13,  17,  19;
31,   23,  37,  29;
41,   43,  47,  59;
61,   53,  67,  79;
71,   73,  97,  89;
101,  83, 107, 109;
131, 103, 127, 139;
151, 113, 137, 149;
181, 163, 157, 179;
... (End)

Maple

N:= 100: # to get the first 4*N terms
A:= Vector(4*N);
for j from 1 to 4 do
  m:= 0;
  for k from 1 while m < N do
    if isprime(10*k+[1, 3, 7, 9][j]) then
      m:= m+1; A[(m-1)*4+j]:= 10*k+[1, 3, 7, 9][j];
    fi
  od
od:
convert(A, list); # Robert Israel, Sep 02 2016

Prog

(PARI) {
n1=10; n3=12; n7=16; n9=18;
for(i=1, 20,
     while(n1%10<>1, n1=nextprime(n1+1)); print1(n1", ");
     while(n3%10<>3, n3=nextprime(n3+1)); print1(n3", ");
     while(n7%10<>7, n7=nextprime(n7+1)); print1(n7", ");
     while(n9%10<>9, n9=nextprime(n9+1)); print1(n9", ");
     n1++; n3++; n7++; n9++;
   )
}
(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

Crossrefs

Cf. A030430, A030431, A030432, A030433.

Sequence in context: A038926 A356466 A168446 * A045798 A267277 A155071

Adjacent sequences: A275464 A275465 A275466 * A275468 A275469 A275470

Keyword

nonn,base,tabf

Author

Dimitris Valianatos, Jul 28 2016

Extensions

Better definition from Omar E. Pol, Jul 29 2016

Status

approved