A253609 Array read by upwards antidiagonals: A(n, k) = index of prime(k)^n in A098550.

2, 4, 3, 6, 5, 9, 14, 19, 11, 15, 29, 57, 94, 40, 22, 65, 171, 483, 269, 124, 23, 137, 549, 2549, 1996, 1071, 187, 30, 277, 1786, 13468, 14547, 12661, 1810, 273, 43, 546, 5563, 69298, 105091, 144229, 24916, 4142, 313, 51, 1109, 17088, 353423, 750571, 1624729, 335764, 74341, 5856, 505, 61

Offset

1,1

Comments

Entry A(n, k), in row n and column k, is the index of the entry in A098550 such that A098550(A(n, k)) = prime(k)^n.

Conjecture: For all natural numbers i, j, k, prime(k)^i precedes prime(k)^(i+1) and prime(k)^j precedes prime(k+1)^j in A098550.

Links

Table of n, a(n) for n=1..55.

Example

Array begins:
   2,    3,     9,     15,       22,       23,        30,        43, ...
   4,    5,    11,     40,      124,      187,       273,       313, ...
   6,   19,    94,    269,     1071,     1810,      4142,      5856, ...
  14,   57,   483,   1996,    12661,    24916,     74341,    116524, ...
  29,  171,  2549,  14547,   144229,   335764,   1300310,   2276597, ...
  65,  549, 13468, 105091,  1624729,  4458533,  22501985,  43999361, ...
 137, 1786, 69298, 750571, 18146462, 58762243, 387122632, 845496081, ...

Crossrefs

Cf. A098550, A251239 (row 1), A251240 (row 2), A251393 (column 1).

Cf. A251241 = {1} union {this array}.

Sequence in context: A232643 A366263 A231334 * A300002 A082560 A191598

Adjacent sequences: A253606 A253607 A253608 * A253610 A253611 A253612

Keyword

nonn,tabl

Author

L. Edson Jeffery, Jan 05 2015

Extensions

More terms from Jinyuan Wang, Jan 26 2025

Status

approved