This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
import Data.List ((\\)) a251549 n = head $ [1, 3 ..] \\ filter odd (take n a098550_list) -- Reinhard Zumkeller, Dec 19 2014
terms = 100;
f[lst_List] := Block[{k=4}, While[GCD[lst[[-2]], k] == 1 || GCD[lst[[-1]], k] > 1 || MemberQ[lst, k], k++]; Append[lst, k]];
A098550 = Nest[f, {1, 2, 3}, terms-3];
a[1] = 3;
a[n_] := a[n] = For[k = a[n-1], True, k = k+2, If[FreeQ[A098550[[1 ;; n]], k], Return[k]]];
Array[a, terms] (* Jean-François Alcover, Aug 02 2018, after Robert G. Wilson v *)
. n p | first 14 multiples of p = prime(n) in A098550, n = 1..25 . -------+------------------------------------------------------------- . 1 2 | 2 4 8 14 6 12 16 10 20 22 26 28 32 18 . 2 3 | 3 9 15 6 12 21 27 39 33 45 51 18 24 36 . 3 5 | 15 5 25 35 10 20 45 85 55 65 30 95 40 50 . 4 7 | 14 35 7 21 28 91 49 63 42 56 77 119 133 161 . 5 11 | 22 11 33 55 44 99 77 66 88 165 143 121 187 110 . 6 13 | 39 13 26 65 91 52 117 78 104 195 143 130 156 221 . 7 17 | 51 17 85 34 68 119 153 102 187 136 170 255 221 204 . 8 19 | 38 19 95 57 133 76 171 114 152 209 247 190 285 228 . 9 23 | 69 23 115 46 161 92 138 207 184 253 299 345 230 276 . 10 29 | 87 29 58 145 203 116 174 261 232 319 377 290 435 348 . 11 31 | 62 31 93 155 124 217 279 186 341 403 248 465 310 372 . 12 37 | 74 37 111 185 148 259 222 333 296 407 555 370 629 481 . 13 41 | 123 41 82 205 164 287 246 369 451 328 410 533 615 492 . 14 43 | 86 43 129 215 172 301 387 258 473 344 430 645 559 516 . 15 47 | 94 47 329 141 235 188 282 423 517 376 470 611 705 564 . 16 53 | 106 53 265 159 212 371 318 477 424 583 689 530 795 636 . 17 59 | 118 59 177 295 236 413 354 531 649 472 767 590 885 1003 . 18 61 | 122 61 427 183 305 244 366 549 671 488 793 610 915 732 . 19 67 | 201 67 335 134 268 469 603 402 536 737 871 670 1005 804 . 20 71 | 142 71 213 355 284 497 426 639 568 781 710 1065 923 852 . 21 73 | 146 73 365 219 292 511 438 657 584 803 730 949 1095 876 . 22 79 | 158 79 237 395 316 553 474 711 632 869 1027 790 1185 948 . 23 83 | 249 83 581 166 415 332 498 747 913 664 1079 830 1245 996 . 24 89 | 178 89 267 445 356 623 534 801 712 979 1157 890 1335 1068 . 25 97 | 291 97 679 194 485 388 582 873 1067 776 970 1261 1455 1164 . . --------------------------------------------------------------------- See also A251715 for a table with T(n,k)/p and A251716 for a table of indices of T(n,k) within A098550.
when seen as table read by rows:
a251637 n k = a251637_tabl !! (n-1) !! (k-1)
a251637_row n= a251637_tabl !! (n-1)
a251637_tabl = adias $ map
(\k -> filter
((== 0) . flip mod (fromInteger $ a000040 k)) a098550_list) [1..]
rows = 25; (* f = A098550 *) Clear[f, row]; f[n_ /; n <= 3] := n; f[n_] := f[n] = Module[{k}, For[k=4, GCD[f[n-2], k] == 1 || GCD[f[n-1], k]>1 || MemberQ[Array[f, n-1], k], k++]; k]; row[n_] := row[n] = Module[{k, cnt}, Reap[For[k=1; cnt=0, cnt <= rows-n, k++, If[Divisible[f[k], Prime[n]], cnt++; Sow[f[k]]]]][[2, 1]]]; A251637 = Table[row[n-k+1][[k]], {n, 1, rows}, {k, 1, n}] // Flatten (* Jean-François Alcover, Dec 17 2014 *)
. n p | Indices of A251637(n,k) in A098550, n = 1..25, k= 1..14 . -------+------------------------------------------------------------- . 1 2 | 2 4 6 8 10 12 14 16 18 20 25 27 29 31 . 2 3 | 3 5 7 10 12 17 19 21 24 26 28 31 33 37 . 3 5 | 7 9 11 13 16 18 26 32 34 36 39 45 48 50 . 4 7 | 8 13 15 17 27 38 40 42 44 58 68 70 72 74 . 5 11 | 20 22 24 34 46 66 68 73 91 100 122 124 126 128 . 6 13 | 21 23 25 36 38 54 83 95 108 120 122 139 178 185 . 7 17 | 28 30 32 35 67 70 111 115 126 141 174 183 185 218 . 8 19 | 41 43 45 47 72 82 113 123 163 166 189 201 221 248 . 9 23 | 49 51 53 56 74 93 149 157 197 228 230 244 252 304 . 10 29 | 59 61 63 96 105 121 188 198 250 259 265 314 323 387 . 11 31 | 60 62 64 98 135 179 200 207 261 263 268 335 343 402 . 12 37 | 77 79 81 118 161 193 241 253 320 348 392 400 411 413 . 13 41 | 85 87 89 146 172 208 266 278 350 358 442 451 478 553 . 14 43 | 86 88 90 148 184 210 280 286 352 369 459 487 489 561 . 15 47 | 99 101 103 109 150 199 306 344 403 406 509 516 538 616 . 16 53 | 112 114 116 131 227 295 349 381 455 470 518 574 610 704 . 17 59 | 125 127 129 219 254 305 389 439 472 511 626 640 697 717 . 18 61 | 130 132 134 136 242 258 396 445 474 531 628 654 726 795 . 19 67 | 140 142 144 147 292 307 458 463 576 581 630 740 772 871 . 20 71 | 151 153 155 287 308 397 469 501 623 636 775 815 837 932 . 21 73 | 156 158 160 162 316 399 480 532 633 686 801 839 865 952 . 22 79 | 165 167 169 289 341 418 515 545 687 690 841 855 917 1033 . 23 83 | 173 175 177 182 321 360 555 577 711 723 843 898 988 1083 . 24 89 | 192 194 196 333 382 512 585 641 771 800 933 972 1075 1155 . 25 97 | 202 204 206 211 370 426 631 695 802 844 1052 1092 1177 1266 . --------------------------------------------------------------------- See table A251637 for A098550(T(n,k)).
seen as table read by rows: a251716 n k = a251716_tabl !! (n-1) !! (k-1) a251716_row n = a251716_tabl !! (n-1) a251716_tabl = map (map a098551) a251637_tabl
a251103 = a006530 . fromIntegral . a098550
a251138 = a001221 . fromIntegral . a098550
a251140 = a001222 . fromIntegral . a098550
a251240 n = a251240_list !! (n-1) a251240_list = filter ((== 2) . a062799 . fromIntegral . a098550) [1..]
from gmpy2 import gcd, is_square, is_prime, isqrt A251240_list, l1, l2, s, b = [], 3, 2, 4, {} for n in range(4,10**4): i = s while True: if not i in b and gcd(i,l1) == 1 and gcd(i,l2) > 1: l2, l1, b[i] = l1, i, 1 while s in b: b.pop(s) s += 1 if is_square(i) and is_prime(isqrt(i)): A251240_list.append(n) break i += 1 print(A251240_list) # Chai Wah Wu, Dec 06 2014
// See Links section.
a251393 n = a251393_list !! (n-1) a251393_list = filter ((== 1) . a209229 . a098550) [1..]
from math import gcd A251393_list, l1, l2, s, p2, b = [1,2], 3, 2, 4, 4, {} for n in range(4,10**4): i = s while True: if not i in b and gcd(i,l1) == 1 and gcd(i,l2) > 1: l2, l1, b[i] = l1, i, 1 while s in b: b.pop(s) s += 1 if i == p2: A251393_list.append(n) p2 *= 2 break i += 1 # Chai Wah Wu, Dec 03 2014
a251557 n = a251557_list !! (n-1)
a251557_list = map (+ 2) $ tail $ scanl maxEven 0 a098550_list
where maxEven u v = if even v then max u v else u
-- Reinhard Zumkeller, Mar 10 2015
terms = 100;
f[lst_] := Block[{k = 4}, While[GCD[lst[[-2]], k] == 1 || GCD[lst[[-1]], k] > 1 || MemberQ[lst, k], k++]; Append[lst, k]];
A098550 = Nest[f, {1, 2, 3}, terms - 3];
a[1] = 2; a[n_] := Max[Select[A098550[[1 ;; n]], EvenQ]] + 2;
Array[a, terms] (* Jean-François Alcover, Aug 02 2018, after Robert G. Wilson v *)
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