A185511 Array: row n shows numbers m such that prime(m) is in row n of the natural number array A000027, by antidiagonals.
1, 4, 2, 5, 3, 6, 10, 7, 11, 8, 12, 9, 34, 17, 13, 19, 15, 44, 29, 20, 18, 22, 28, 80, 37, 23, 25, 14, 33, 40, 95, 55, 60, 67, 21, 16, 43, 51, 143, 85, 76, 110, 31, 30, 46, 47, 71, 221, 109, 194, 127, 45, 41, 145, 26, 59, 91, 243, 155, 252, 181, 61, 52, 244, 38, 24, 75, 103, 314, 175, 349, 202, 63, 72, 316, 42, 32, 27
Offset: 1
Examples
Start with the natural number array A000027: 1...2...4...7 3...5...8..12 6...9..13..18 (The antidiagonals are 1; 2,3; 4,5,6; 7,8,9,10;...). Primes, by rows (A185510): 2.....7....11....29... in row 1 of A000027 3.....5....17....23... in row 2 13...31...139...193... in row 3, etc. Now replace each prime by its index to obtain A185511. Northwest corner: 1.....4....5...10...12...19...22...33 2.....3....7....9...15...28...40...51 6....11...34...44...80...95..143..221 8....17...29...37...55...85..109..155 13...20...23...60...76..194..252..349
Programs
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Mathematica
f[n_,k_]:=n+(k+n-2) (k+n-1)/2; Do[t[n]={};Do[If[PrimeQ[f[n,k]],AppendTo[t[n],f[n,k]]],{k,1,1000}]; t[n]; u[n]={};Do[If[MemberQ[t[n],Prime[m]],AppendTo[u[n],m]],{m,1,1000}],{n,12}] TableForm[Table[u[n],{n,12}]]
Comments