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

0, 1, 3, 5, 3, 13, 9, 15, 21, 29, 3, 33, 45, 21, 39, 45, 69, 99, 105, 111, 15, 27, 57, 75, 93, 117, 153, 177, 183, 243, 253, 9, 45, 81, 129, 165, 231, 249, 261, 285, 315, 345, 375, 399, 441, 459, 465, 471, 501

Offset

1,3

Comments

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.

Links

Table of n, a(n) for n=1..49.

Example

Triangle starting with T(1,1):
0
1
3  5
3  13
9  15 21 29
3  33 45
21 39 45 69  99  105 111
15 27 57 75  93  117 153 177 183 243 253
9  45 81 129 165 231 249 261 285 315 345 375 399 441 459 465 471 501
...
T(5,4)=29 because 2^5=32; 32+29=61 and 32-29=3 are prime.

Crossrefs

Cf. A000040 (prime numbers).

Sequence in context: A089948 A336806 A023583 * A121278 A023587 A172003

Adjacent sequences: A266600 A266601 A266602 * A266604 A266605 A266606

Keyword

nonn,tabf

Author

Bob Selcoe, Feb 21 2016

Status

approved