A216288 Prime-free decades such that the next decade is also prime-free.

113, 133, 134, 167, 218, 248, 314, 323, 347, 374, 418, 430, 476, 484, 512, 524, 536, 545, 560, 575, 596, 640, 650, 674, 692, 708, 713, 726, 737, 776, 797, 833, 839, 847, 848, 890, 907, 935, 944, 956, 998, 1001, 1004, 1037, 1040, 1080, 1081, 1091, 1133, 1175

Offset: 1

Author

V. Raman, Sep 03 2012

Keywords

• nonn
• base

Comments

Numbers n such that 10n+1, 10n+3, 10n+7, 10n+9, 10n+11, 10n+13, 10n+17, and 10n+19 are composite. - Charles R Greathouse IV, Sep 07 2012

Links

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

Crossrefs

Cf. A190639, A032352.

Cf. A219998 (upper decade).

Programs

Magma

/* After the Greathouse's comment: */ [n: n in [0..1200] | forall{10*n+i: i in [1,3,7,9,11,13,17,19] | not IsPrime(10*n+i)}]; // Bruno Berselli, Sep 14 2012

Mathematica

ps0 = {2, 3, 5, 7}; t = {}; Do[ps1 = Select[Range[10*n, 10*n + 9], PrimeQ]; If[Length[ps0] == Length[ps1] == 0, AppendTo[t, n-1]]; ps0 = ps1, {n, 2, 1000}]; t (* T. D. Noe, Sep 03 2012 *)

PARI

is(n)=nextprime(10*n)-10*n>20 \\ Charles R Greathouse IV, Sep 07 2012

PARI

is(n)=!(isprime(10*n+1) || isprime(10*n+3) || isprime(10*n+7) || isprime(10*n+9) || isprime(10*n+11) || isprime(10*n+13) || isprime(10*n+17) || isprime(10*n+19)) \\ Charles R Greathouse IV, Sep 07 2012

PARI

for(i=2, 1200, if(isprime(10*i+1)==0&&isprime(10*i+3)==0&&isprime(10*i+7)==0&&isprime(10*i+9)==0&&isprime(10*i+11)==0&&isprime(10*i+13)==0&&isprime(10*i+17)==0&&isprime(10*i+19)==0, print1(i", "))) /* V. Raman, Dec 08 2012 */

Formula

a(n) ~ n. - Charles R Greathouse IV, Sep 07 2012

a(n) = A219998(n) - 1. - V. Raman, Dec 08 2012