A376893 Square array read by antidiagonals in ascending order where T(n,k), n>1 and k>=1, is the least prime p, writtten in base n, starting a run of exactly k consecutive primes with non increasing sum of digits.

2, 3, 3, 2, 2, 11, 2, 3, 7, 7, 2, 3, 11, 5, 647, 2, 5, 23, 79, 239, 823, 2, 5, 29, 19, 647, 233, 6299, 2, 7, 19, 137, 463, 40427, 1699, 6287, 2, 7, 31, 251, 11003, 11617, 102811, 1697, 150247, 2, 7, 89, 751, 241, 46187, 11597, 107507, 10037, 150239, 2, 7, 89, 241, 947, 1747, 248987, 11593, 378023, 67741, 1610941

Offset

2,1

Links

Table of n, a(n) for n=2..67.

Example

The prime numbers 7 and 11 are consecutive primes. In base 10, the sum of the digits of 7 and 11 are respectively 7 and 2. Since  7 is greater than or equal to 2, and there are no smaller numbers with this property, we have T(10,2) = 7.
The prime numbers 11, 13, 17 are consecutive primes. In base 2, the sum of the digits of 11 = 1011_2 and 13 = 1101_2 is 3 and the sum of digits of 17 = 10001_2 is 2. Since 3 >= 3 >= 2, and there are no smaller numbers with this property, we have T(2,3) = 11.
The top left corner of the array begins at T(2,1):
     2      3     11      7    647    823  ...
     3      2      7      5    239    233  ...
     2      3     11     79    647  40427  ...
     2      3     23     19    463  11617  ...
     2      5     29    137  11003  46187  ...
   ...    ...    ...    ...    ...    ...  ...

Crossrefs

Cf. A007953.

Sequence in context: A130631 A282014 A241539 * A213512 A218774 A270824

Adjacent sequences: A376890 A376891 A376892 * A376894 A376895 A376896

Keyword

tabl,nonn,base

Author

Jean-Marc Rebert, Oct 08 2024

Status

approved