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 A266603 Irregular triangle T(n,k) read by rows: numbers such that 2^n +/- T(n,k) are both primes. 0

%I #27 Feb 23 2016 11:49:25

%S 0,1,3,5,3,13,9,15,21,29,3,33,45,21,39,45,69,99,105,111,15,27,57,75,

%T 93,117,153,177,183,243,253,9,45,81,129,165,231,249,261,285,315,345,

%U 375,399,441,459,465,471,501

%N Irregular triangle T(n,k) read by rows: numbers such that 2^n +/- T(n,k) are both primes.

%C Except when k is maximum for a given n, all elements must be odd multiples of 3. Specifically: T(n,k) == {9,15,21} mod 30 when n is odd and T(n,k) == {3,15,27} mod 30 when n is even. The only exception is T(3,1)=3.

%e Triangle starting with T(1,1):

%e 0

%e 1

%e 3 5

%e 3 13

%e 9 15 21 29

%e 3 33 45

%e 21 39 45 69 99 105 111

%e 15 27 57 75 93 117 153 177 183 243 253

%e 9 45 81 129 165 231 249 261 285 315 345 375 399 441 459 465 471 501

%e ...

%e T(5,4)=29 because 2^5=32; 32+29=61 and 32-29=3 are prime.

%Y Cf. A000040 (prime numbers).

%K nonn,tabf

%O 1,3

%A _Bob Selcoe_, Feb 21 2016

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Last modified May 31 15:55 EDT 2023. Contains 363068 sequences. (Running on oeis4.)