A324156 Irregular triangle T(n,k) read by rows in which row n lists the numbers m such that the number of prime numbers <= m is equal to the number of base-n zerofree numbers <= m.

2, 3, 4, 3, 113, 114, 115, 116, 117, 118, 119, 120, 199, 200, 201, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 482, 483, 491, 492, 493, 494, 495, 496, 497, 498, 344251, 344252, 344253, 344254, 344255, 344256, 351902, 353501, 353502, 353503

Offset

2,1

Comments

The offset is 2 since the least base (= row) for which the definition makes sense is n = 2.

The least term of row n is T(n,1) = A324154(n). The last term of row n is T(n,j) = A324155(n), where j = A324157(n) is the number of terms of the n-th row.

Terms of rows higher than 5 are unknown, but they are bounded by the above rule. For example, the first term of the 6th row is T(6,1) = A324154(n) = 4.1645*10^15, approximately. The last term of the 6th row is A324155(n) = 1.46705*10^16, approximately.

Links

Table of n, a(n) for n=2..50.

Example

T(2,1) = 2, since pi(2) = 1 = numOfZerofreeNum_2(2) where numOfZerofreeNum_n(k) = number of base-n zerofree numbers <= k.
T(2,2) = 3, since pi(3) = 2 = numOfZerofreeNum_2(3).
T(3,2) = 4, since pi(4) = 2 = numOfZerofreeNum_2(3).
T(3,1) = 3, since pi(3) = 2 = numOfZerofreeNum_3(3).
T(3,2) = 113, since pi(113) = 30 = numOfZerofreeNum_3(113).
Triangle T(n,k) begins:
2, 3, 4;
3, 113, 114, 115, 116, 117, 118, 119, 120, 199, 200, 201, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 482, 483, 491, 492, 493, 494, 495, 496, 497, 498;
344251, 344252, 344253, 344254, 344255, 344256, 351902, 353501, 353502, 353503, 353504, 353505, 353506, 353507, 353508, 353509, 353510, 353511, 353512, 353513, 353514, 353515, 353516, 353517, 353518, 353519, 353520, 353521, 353522, 353523, 353524, 353525, 353526, 353631, 353632, 353633, 353634, 353635, 353636, 601379, 601380, 601381, 601382, 601383, 601384, 601385, 601386, 601387, 601388, 601389, 601390, 601391, 601392, 601393, 601394, 601395, 601396, 617903, 617904, 617905, 617906, 617907, 617908, 867281, 867282, 867283, 867284, 867285, 867286, 867287, 867288, 867289, 867290, 867291, 867292, 867293, 867294, 867295, 867296, 867297, 867298, 867299, 867300, 876414, 876431, 876432, 876437, 877213, 877214, 877215, 877216, 877217, 877218, 877219, 877220, 877221, 877222, 878014, 878021, 878022, 878037, 1139549, 1139550, 1139551, 1139552, 1139553, 1139554, 1139555, 1139556;
33182655683, 33182655684, 33182655685, 33182655686, 33182655687, 33182655688;

Crossrefs

Cf. A324160, A324161, A324154, A324155, A324157.

Sequence in context: A009590 A009492 A009810 * A111362 A134581 A099587

Adjacent sequences: A324153 A324154 A324155 * A324157 A324158 A324159

Keyword

nonn,base,tabf

Author

Hieronymus Fischer, Jul 16 2019

Status

approved