Decades in which 4 primes occur.
0, 1, 10, 19, 82, 148, 187, 208, 325, 346, 565, 943, 1300, 1564, 1573, 1606, 1804, 1891, 1942, 2101, 2227, 2530, 3172, 3484, 4378, 5134, 5533, 6298, 6721, 6949, 7222, 7726, 7969, 8104, 8272, 8881, 9784, 9913, 10111, 10984, 11653, 11929, 12220, 13546, 14416
1
The zeroth decade is the only decade having an even number. In all other decades d, the primes consist of the pair of twin primes 10*d + 1, 10*d + 3, 10*d + 7, and 10*d + 9.
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
Eric W. Weisstein, Prime Quadruplet
(Mma) Join[{0}, Select[Range[15000], PrimeQ[10 # + 1] && PrimeQ[10 # + 3] && PrimeQ[10 # + 7] && PrimeQ[10 # + 9] &]]
Cf. A007811 (pairs of twins), A008471 (3 primes), A032352 (no primes), A216292 (1 prime), A216293 (2 primes).
nonn,base
T. D. Noe, Oct 19 2016