login
A231609
Table whose n-th row consists of primes p such that p + 2n is the next prime, read by antidiagonals.
1
3, 7, 5, 23, 13, 11, 89, 31, 19, 17, 139, 359, 47, 37, 29, 199, 181, 389, 53, 43, 41, 113, 211, 241, 401, 61, 67, 59, 1831, 293, 467, 283, 449, 73, 79, 71, 523, 1933, 317, 509, 337, 479, 83, 97, 101, 887, 1069, 2113, 773, 619, 409, 491, 131, 103, 107
OFFSET
1,1
COMMENTS
The plot has an unusual gap near 10^5. Why?
EXAMPLE
The following sequences are read by antidiagonals
{ 3, 5, 11, 17, 29, 41, 59, 71, 101, 107, ...}
{ 7, 13, 19, 37, 43, 67, 79, 97, 103, 109, ...}
{ 23, 31, 47, 53, 61, 73, 83, 131, 151, 157, ...}
{ 89, 359, 389, 401, 449, 479, 491, 683, 701, 719, ...}
{ 139, 181, 241, 283, 337, 409, 421, 547, 577, 631, ...}
{ 199, 211, 467, 509, 619, 661, 797, 997, 1201, 1237, ...}
{ 113, 293, 317, 773, 839, 863, 953, 1409, 1583, 1847, ...}
{1831, 1933, 2113, 2221, 2251, 2593, 2803, 3121, 3373, 3391, ...}
{ 523, 1069, 1259, 1381, 1759, 1913, 2161, 2503, 2861, 3803, ...}
{ 887, 1637, 3089, 3413, 3947, 5717, 5903, 5987, 6803, 7649, ...}
...
MATHEMATICA
nn = 10; t = Table[{}, {nn}]; complete = 0; lastP = 3; While[complete < nn, p = NextPrime[lastP]; diff = p - lastP; If[diff <= 2*nn && Length[t[[diff/2]]] < nn - diff/2 + 1, AppendTo[t[[diff/2]], lastP]; If[Length[t[[diff/2]]] == nn - diff/2 + 1, complete++]]; lastP = p]; t2 = PadRight[t, {nn, nn}, 0]; Table[t2[[n-j+1, j]], {n, nn}, {j, n}]
CROSSREFS
Cf. A000230 (numbers in first column).
Sequence in context: A305421 A354544 A112071 * A046561 A112927 A097406
KEYWORD
nonn,tabl,look
AUTHOR
T. D. Noe, Nov 26 2013
STATUS
approved