A216329 Decades whose prime pattern is the same as the prime pattern in the next decade, with at least one prime.

37, 78, 124, 139, 154, 180, 234, 276, 288, 291, 310, 331, 436, 444, 499, 532, 558, 609, 616, 624, 648, 696, 706, 717, 750, 820, 856, 873, 894, 951, 961, 973, 1047, 1072, 1099, 1114, 1188, 1270, 1309, 1347, 1351, 1356, 1366, 1383, 1414, 1419, 1429, 1447, 1473

Offset: 1

Author

V. Raman, Sep 04 2012

Keywords

• nonn
• base

Links

• V. Raman, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A190639.

Cf. A219997 (upper decade).

Programs

Mathematica

ps0 = {2, 3, 5, 7}; n = 0; t = {}; While[Length[t] < 50, n++; ps1 = Select[Range[10 n, 10 n + 9], PrimeQ]; If[Length[ps0] > 0 && Length[ps0] == Length[ps1] && ps0 + 10 == ps1, AppendTo[t, n - 1]]; ps0 = ps1]; t (* T. D. Noe, Sep 04 2012 *)

PARI

isok(i) = { isprime(10*i+1)==isprime(10*i+11) && isprime(10*i+3)==isprime(10*i+13) && isprime(10*i+7)==isprime(10*i+17) && isprime(10*i+9)==isprime(10*i+19) && isprime(10*i+1)+isprime(10*i+3)+isprime(10*i+7)+isprime(10*i+9)>=1 } \\ V. Raman, Dec 08 2012

Formula

a(n) >> n log^2 n. - Charles R Greathouse IV, Sep 06 2012

a(n) = A219997(n) - 1. - V. Raman, Dec 08 2012