login
A097586
Table T(n,n) read by rows: T(1,1)=0; then if n even T(n,1)=T(n-1,1)+2 and if n odd T(n,1)=T(n-2,1)+T(n-1,1)-1 then T(n,j)=T(n,j-1) + 2^floor((n+1)/2).
1
0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 3, 11, 19, 27, 35, 43, 51, 59, 67, 75, 5, 13, 21, 29, 37, 45, 53, 61, 69, 77, 7, 23, 39, 55, 71, 87, 103, 119, 135, 151, 9, 25, 41, 57, 73
OFFSET
1,2
COMMENTS
Integers > 1 appear exactly twice, 0 and 1 only once. Consecutive primes with gap 4 are consecutive in rows 3 or 4
The sequence contains the first 10 elements of row n=1, then the first 10 elements of row n=2, then the first 10 elements of row n=3 etc. The array is not read in full, not by diagonals and not as a lower or upper triangle. - R. J. Mathar, May 01 2024
EXAMPLE
0 2 4 6 8 10 12 14 16 18
2 4 6 8 10 12 14 16 18 20
1 5 9 13 17 21 25 29 33 37
3 7 11 15 19 23 27 31 35 39
3 11 19 27 35 43 51 59 67 75
5 13 21 29 37 45 53 61 69 77
7 23 39 55 71 87 103 119 135 151
9 25 41 57 73 89 105 121 137 153
15 47 79 111 143 175 207 239 271 303
17 49 81 113 145 177 209 241 273 305
31 95 159 223 287 351 415 479 543 607
33 97 161 225 289 353 417 481 545 609
63 191 319 447 575 703 831 959 1087 1215
65 193 321 449 577 705 833 961 1089 1217
127 383 639 895 1151 1407 1663 1919 2175 2431
129 385 641 897 1153 1409 1665 1921 2177 2433
255 767 1279 1791 2303 2815 3327 3839 4351 4863
257 769 1281 1793 2305 2817 3329 3841 4353 4865
MAPLE
A097586 := proc(n, k)
if n < 1 then
0 ;
elif k < 1 then
0 ;
elif k = 1 then
if n = 1 then
0;
elif type(n, 'even') then
procname(n-1, 1)+2 ;
else
procname(n-2, 1)+procname(n-1, 1)-1 ;
end if;
else
procname(n, k-1)+2^floor((n+1)/2) ;
end if;
end proc:
for n from 1 to 18 do
for k from 1 to 10 do
printf("%5d ", A097586(n, k)) ;
end do:
printf("\n") ;
end do: # R. J. Mathar, May 01 2024
CROSSREFS
Sequence in context: A061762 A136614 A245627 * A169805 A340479 A263042
KEYWORD
nonn,less
AUTHOR
Pierre CAMI, Sep 20 2004
STATUS
approved