A375765 Square array read by antidiagonals in ascending order T(n,k), n > 1 and k > 0, representing the least prime p that starts a run of exactly k consecutive primes, all having the same sum of digits in base n > 1, or -1 if no such number exists.

2, 2, 3, 2, 11, 7, 2, 23, 7, 167, 2, 7, 151, 5, 941, 2, 139, 479, 1901, 1019, 6299, 2, 23, 8543, 467, 12823, 1013, 6287, 2, 293, 151, 123239, 463, 102811, 4391, 150287, 2, 89, 23929, 251, 2350349, 15667, 369991, 8849, 866087, 2, 523, 1823, 370247, 1747, 24370007

Offset

2,1

Links

Table of n, a(n) for n=2..52.

Example

T(2,3) = 7, because the 3 consecutive primes 7 = 111_2, 11 = 1011 and 13 = 1101_2 have all the same sum of digits in base 2, and no lesser number has this property.
The upper left square of the table begins at T(2,1):
  2   3    7    167     941     6299 ...
  2  11    7      5    1019     1013 ...
  2  23  151   1901   12823   102811 ...
  2   7  479    467     463    15667 ...
  2 139 8543 123239 2350349 24370007 ...
  2  23  151    251    1747     1741 ...
... ...  ...    ...     ...      ... ...

Crossrefs

Cf. A071613.

Sequence in context: A087139 A342607 A226422 * A016005 A016006 A285247

Adjacent sequences: A375762 A375763 A375764 * A375766 A375767 A375768

Keyword

nonn,base,tabl

Author

Jean-Marc Rebert, Aug 27 2024

Status

approved