A230852 Smallest k<3*2^n such that 3*2^n+k is the smallest of four consecutive primes in arithmetic progression or 0 if no solution.

0, 0, 0, 0, 0, 59, 0, 0, 205, 229, 167, 353, 1595, 4459, 6407, 6215, 14995, 4559, 4697, 11399, 365, 10199, 19327, 39103, 3185, 13649, 15787, 2693, 21455, 24929, 32209, 30509, 13421, 5389, 36947, 12869, 27277, 38389, 973, 69199, 58835, 165629, 52597, 25463, 17923, 38629, 90263, 17153, 48143, 2171, 1255

Offset

1,6

Comments

Conjecture: if n>8 there is always a solution.

Links

Pierre CAMI, Table of n, a(n) for n = 1..110

Example

3*2^6+59=251, and 251, 257, 263, 269 are four consecutive primes in arithmetic progression 6 so a(6)=59.
3*2^9+205=1741, and 1741, 1747, 1753, 1759 are four consecutive primes in arithmetic progression 6 so a(9)=205.

Prog

(PARI) cpap4(p)=my(q=nextprime(p+1), g=q-p); nextprime(q+1)-q==g&&nextprime(p+2*g+1)==p+3*g
a(n)=forprime(p=3<<n, 6<<n, if(cpap4(p), return(p-3<<n))) \\ Charles R Greathouse IV, Oct 31 2013

Crossrefs

Cf. A054800, A230699.

Sequence in context: A201988 A116103 A116115 * A104380 A051321 A235774

Adjacent sequences: A230849 A230850 A230851 * A230853 A230854 A230855

Keyword

nonn

Author

Pierre CAMI, Oct 31 2013

Status

approved