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.
%I A297709 #28 Jan 25 2022 13:02:27
%S A297709 3,5,7,7,13,3,11,19,5,23,13,23,11,31,7,17,31,17,47,13,5,19,37,29,53,
%T A297709 19,11,3,23,43,41,61,37,17,0,89,29,47,59,73,43,29,0,113,23,31,53,71,
%U A297709 83,67,41,0,139,31,19,37,61,101,89,79,59,0,181,47,43,7,41,67
%N A297709 Table read by antidiagonals: Let b be the number of digits in the binary expansion of n. Then T(n,k) is the k-th odd prime p such that the binary digits of n match the primality of the b consecutive odd numbers beginning with p (or 0 if no such k-th prime exists).
%C A297709 For each n >= 1, row n is the union of rows 2n and 2n+1.
%C A297709 Rows with no nonzero terms: 15, 21, 23, 28, 30, 31, ...
%C A297709 Rows whose only nonzero term is 3: 7, 14, 29, 59, 118, 237, 475, 950, 1901, 3802, 7604, ...
%C A297709 Rows whose only nonzero term is 5: 219, 438, 877, 1754, 3508, 7017, 14035, ...
%C A297709 For j = 2, 3, 4, ..., respectively, the first row whose only nonzero term is prime(j) is 7, 219, 2921, ...; is there such a row for every odd prime?
%e A297709 13 = 1101_2, so row n=13 lists the odd primes p such that the four consecutive odd numbers p, p+2, p+4, and p+6 are prime, prime, composite, and prime, respectively; these are the terms of A022004.
%e A297709 14 = 1110_2, so row n=14 lists the odd primes p such that p, p+2, p+4, and p+6 are prime, prime, prime, and composite, respectively; since there is only one such prime (namely, 3), there is no such 2nd, 3rd, 4th, etc. prime, so the terms in row 14 are {3, 0, 0, 0, ...}.
%e A297709 15 = 1111_2, so row n=15 would list the odd primes p such that p, p+2, p+4, and p+6 are all prime, but since no such prime exists, every term in row 15 is 0.
%e A297709 Table begins:
%e A297709 n in base| k | OEIS
%e A297709 ---------+----------------------------------------+sequence
%e A297709 10 2 | 1 2 3 4 5 6 7 8 | number
%e A297709 =========+========================================+========
%e A297709 1 1 | 3 5 7 11 13 17 19 23 | A065091
%e A297709 2 10 | 7 13 19 23 31 37 43 47 | A049591
%e A297709 3 11 | 3 5 11 17 29 41 59 71 | A001359
%e A297709 4 100 | 23 31 47 53 61 73 83 89 | A124582
%e A297709 5 101 | 7 13 19 37 43 67 79 97 | A029710
%e A297709 6 110 | 5 11 17 29 41 59 71 101 | A001359*
%e A297709 7 111 | 3 0 0 0 0 0 0 0 |
%e A297709 8 1000 | 89 113 139 181 199 211 241 283 | A083371
%e A297709 9 1001 | 23 31 47 53 61 73 83 131 | A031924
%e A297709 10 1010 | 19 43 79 109 127 163 229 313 |
%e A297709 11 1011 | 7 13 37 67 97 103 193 223 | A022005
%e A297709 12 1100 | 29 59 71 137 149 179 197 239 | A210360*
%e A297709 13 1101 | 5 11 17 41 101 107 191 227 | A022004
%e A297709 14 1110 | 3 0 0 0 0 0 0 0 |
%e A297709 15 1111 | 0 0 0 0 0 0 0 0 |
%e A297709 16 10000 | 113 139 181 199 211 241 283 293 | A124584
%e A297709 17 10001 | 89 359 389 401 449 479 491 683 | A031926
%e A297709 18 10010 | 31 47 61 73 83 151 157 167 |
%e A297709 19 10011 | 23 53 131 173 233 263 563 593 | A049438
%e A297709 20 10100 | 19 43 79 109 127 163 229 313 |
%e A297709 21 10101 | 0 0 0 0 0 0 0 0 |
%e A297709 22 10110 | 7 13 37 67 97 103 193 223 | A022005
%e A297709 23 10111 | 0 0 0 0 0 0 0 0 |
%e A297709 24 11000 | 137 179 197 239 281 419 521 617 |
%e A297709 25 11001 | 29 59 71 149 269 431 569 599 | A049437*
%e A297709 26 11010 | 17 41 107 227 311 347 461 641 |
%e A297709 27 11011 | 5 11 101 191 821 1481 1871 2081 | A007530
%e A297709 28 11100 | 0 0 0 0 0 0 0 0 |
%e A297709 29 11101 | 3 0 0 0 0 0 0 0 |
%e A297709 30 11110 | 0 0 0 0 0 0 0 0 |
%e A297709 31 11111 | 0 0 0 0 0 0 0 0 |
%e A297709 *other than the referenced sequence's initial term 3
%e A297709 .
%e A297709 Alternative version of table:
%e A297709 .
%e A297709 n in base|primal-| k | OEIS
%e A297709 ---------+ ity +------------------------------+ seq.
%e A297709 10 2 |pattern| 1 2 3 4 5 6 | number
%e A297709 =========+=======+==============================+========
%e A297709 1 1 | p | 3 5 7 11 13 17 | A065091
%e A297709 2 10 | pc | 7 13 19 23 31 37 | A049591
%e A297709 3 11 | pp | 3 5 11 17 29 41 | A001359
%e A297709 4 100 | pcc | 23 31 47 53 61 73 | A124582
%e A297709 5 101 | pcp | 7 13 19 37 43 67 | A029710
%e A297709 6 110 | ppc | 5 11 17 29 41 59 | A001359*
%e A297709 7 111 | ppp | 3 0 0 0 0 0 |
%e A297709 8 1000 | pccc | 89 113 139 181 199 211 | A083371
%e A297709 9 1001 | pccp | 23 31 47 53 61 73 | A031924
%e A297709 10 1010 | pcpc | 19 43 79 109 127 163 |
%e A297709 11 1011 | pcpp | 7 13 37 67 97 103 | A022005
%e A297709 12 1100 | ppcc | 29 59 71 137 149 179 | A210360*
%e A297709 13 1101 | ppcp | 5 11 17 41 101 107 | A022004
%e A297709 14 1110 | pppc | 3 0 0 0 0 0 |
%e A297709 15 1111 | pppp | 0 0 0 0 0 0 |
%e A297709 16 10000 | pcccc | 113 139 181 199 211 241 | A124584
%e A297709 17 10001 | pcccp | 89 359 389 401 449 479 | A031926
%e A297709 18 10010 | pccpc | 31 47 61 73 83 151 |
%e A297709 19 10011 | pccpp | 23 53 131 173 233 263 | A049438
%e A297709 20 10100 | pcpcc | 19 43 79 109 127 163 |
%e A297709 21 10101 | pcpcp | 0 0 0 0 0 0 |
%e A297709 22 10110 | pcppc | 7 13 37 67 97 103 | A022005
%e A297709 23 10111 | pcppp | 0 0 0 0 0 0 |
%e A297709 24 11000 | ppccc | 137 179 197 239 281 419 |
%e A297709 25 11001 | ppccp | 29 59 71 149 269 431 | A049437*
%e A297709 26 11010 | ppcpc | 17 41 107 227 311 347 |
%e A297709 27 11011 | ppcpp | 5 11 101 191 821 1481 | A007530
%e A297709 28 11100 | pppcc | 0 0 0 0 0 0 |
%e A297709 29 11101 | pppcp | 3 0 0 0 0 0 |
%e A297709 30 11110 | ppppc | 0 0 0 0 0 0 |
%e A297709 31 11111 | ppppp | 0 0 0 0 0 0 |
%e A297709 .
%e A297709 *other than the referenced sequence's initial term 3
%Y A297709 Cf. A001359, A007530, A022004, A022005, A029710, A031924, A031926, A049437, A049438, A049591, A065091, A124582, A083371, A124584, A210360.
%K A297709 nonn,tabl
%O A297709 1,1
%A A297709 _Jon E. Schoenfield_, Apr 15 2018