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A356226 lists maximal gapless interval lengths of prime indices.
- length: A287170
- bisected length: A356229
- Heinz number: A356231
- firsts: A356232
Cf. `A000005, `A001222, `A060680, `A060681, `~A066205, A119313, ~`A137921, `A193829, `A287170, ~`A328023, ~`A328335, `~A328336, ~`A328457, ~`A328458, A356226, `A356229, ~`A356231, `A356232.
A permutation of the positive integers > 1.
This is a permutation of the positive integers > 1.
nn=1000;
mnrm[s_]:=If[Min@@s==1, mnrm[DeleteCases[s-1, 0]]+1, 0];
gapa=Differences[Array[Prime, nn10000]];
mn=Select[Range[nn], Count[gapa, #]>1&];
Table[Position[gapa, 2*(k-n+1)][[n, 1]], {k, mnrm[mn/2]6}, {n, k}]
This sequence The diagonal A(n,n) is A356222A356223.
Diagonal A(n,n) is A356223.
A356224 counts even divisors with gapless prime indices, complement A356225.
- minimum: A356227
- maximum: A356228
- standard composition: A356230
- positions of first appearances: A356232
Cf. A000005 divs, A001222 om, A056239 heinz_wt, A060680 min_divgap, A060681 max_divgap, A060766 lcm_divgaps, A066205 firsts_num_max_gapless, A112798 list_of_mults, A119313 third_div_pri, A137921 numof_div_runs, A193829 tri_divgap.
Cf. A328023 h_of_divgap_of_n, A328335 consec_prix_relpri, A328336 no_consec_relpri, A328457 maxrun_divs_grtr1, A328458 max_divrun_nontriv.
- firsts: A356232
Cf. `A000005, `A001222, `A060680, `A060681, `~A066205, A119313, ~`A137921, `A193829, ~`A328023, ~`A328335, `~A328336, ~`A328457, ~`A328458.
2, 4, 3, 9, 6, 5, 24, 11, 8, 7, 34, 72, 15, 12, 10, 46, 42, 77, 16, 14, 13, 30, 47, 53, 79, 18, 19, 17, 282, 62, 91, 61, 87, 21, 22, 20, 99, 295, 66, 97, 68, 92, 23, 25, 26, 154, 180, 319, 137, 114, 80, 94, 32, 27, 28, 189, 259, 205, 331, 146, 121, 82, 124, 36, 29, 33
1,1
A permutation of the positive integers > 1.
Prime gaps (A001223) are the differences between consecutive prime numbers. They begin: 1, 2, 2, 4, 2, 4, 2, 4, 6, ...
Array begins:
k=1 k=2 k=3 k=4 k=5 k=6 k=7 k=8 k=9
n=1: 2 3 5 7 10 13 17 20 26
n=2: 4 6 8 12 14 19 22 25 27
n=3: 9 11 15 16 18 21 23 32 36
n=4: 24 72 77 79 87 92 94 124 126
n=5: 34 42 53 61 68 80 82 101 106
n=6: 46 47 91 97 114 121 139 168 197
n=7: 30 62 66 137 146 150 162 223 250
n=8: 282 295 319 331 335 378 409 445 476
n=9: 99 180 205 221 274 293 326 368 416
For example, the positions in A001223 of appearances of 2*3 are A320701 = 9, 11, 15, 16, 18, 21, 23, ..., which is row n = 3.
nn=1000;
mnrm[s_]:=If[Min@@s==1, mnrm[DeleteCases[s-1, 0]]+1, 0];
gapa=Differences[Array[Prime, nn]];
mn=Select[Range[nn], Count[gapa, #]>1&];
Table[Position[gapa, 2*(k-n+1)][[n, 1]], {k, mnrm[mn/2]}, {n, k}]
The row containing n is A028334(n).
Row n = 1 is A029707.
Row n = 2 is A029709.
Column k = 1 is A038664.
The column containing n is A274121(n).
Column k = 2 is A356221.
This sequence is A356222.
Diagonal A(n,n) is A356223.
A001223 lists the prime gaps.
A073491 lists numbers with gapless prime indices.
A356224 counts divisors with gapless prime indices, complement A356225.
A356226 lists maximal gapless interval lengths of prime indices.
- length: A287170
- minimum: A356227
- maximum: A356228
- bisected length: A356229
- standard composition: A356230
- Heinz number: A356231
- positions of first appearances: A356232
Cf. A000005 divs, A001222 om, A056239 heinz_wt, A060680 min_divgap, A060681 max_divgap, A060766 lcm_divgaps, A066205 firsts_num_max_gapless, A112798 list_of_mults, A119313 third_div_pri, A137921 numof_div_runs, A193829 tri_divgap.
Cf. A328023 h_of_divgap_of_n, A328335 consec_prix_relpri, A328336 no_consec_relpri, A328457 maxrun_divs_grtr1, A328458 max_divrun_nontriv.
allocated
nonn,tabl
Gus Wiseman, Aug 04 2022
approved
editing
allocated for Gus Wiseman
allocated
approved