A356155 The pi-based arithmetic derivative applied to prime shift array: Square array A(n,k) = A258851(A246278(n,k)), read by falling antidiagonals.
1, 4, 2, 7, 12, 3, 12, 19, 30, 4, 11, 54, 41, 56, 5, 20, 26, 225, 79, 110, 6, 15, 87, 58, 588, 131, 156, 7, 32, 37, 310, 94, 1815, 193, 238, 8, 33, 216, 69, 861, 162, 3042, 269, 304, 9, 32, 140, 1500, 117, 2156, 218, 6069, 355, 414, 10, 21, 120, 427, 5488, 183, 3835, 314, 8664, 491, 580, 11, 52, 44, 455, 1254, 26620, 255, 6834, 422, 14283, 629, 682, 12
Offset: 1
Examples
The top left corner of the array: k = 1 2 3 4 5 6 7 8 9 10 11 12 2k = 2 4 6 8 10 12 14 16 18 20 22 24 -----+-------------------------------------------------------------------------- n= 1 | 1, 4, 7, 12, 11, 20, 15, 32, 33, 32, 21, 52, 2 | 2, 12, 19, 54, 26, 87, 37, 216, 140, 120, 44, 351, 3 | 3, 30, 41, 225, 58, 310, 69, 1500, 427, 455, 86, 2075, 4 | 4, 56, 79, 588, 94, 861, 117, 5488, 1254, 1022, 132, 8183, 5 | 5, 110, 131, 1815, 162, 2156, 183, 26620, 2561, 2717, 214, 31581, 6 | 6, 156, 193, 3042, 218, 3835, 255, 52728, 4828, 4316, 304, 67093, 7 | 7, 238, 269, 6069, 314, 6834, 373, 137564, 7695, 8075, 404, 154615, 8 | 8, 304, 355, 8664, 422, 10241, 457, 219488, 12098, 12426, 524, 261003, 9 | 9, 414, 491, 14283, 532, 17296, 609, 438012, 20909, 18653, 668, 535877, 10 | 10, 580, 629, 25230, 718, 27231, 787, 975560, 29388, 31552, 836, 1050409,
Links
Programs
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PARI
up_to = 78; A246278sq(row,col) = if(1==row,2*col, my(f = factor(2*col)); for(i=1, #f~, f[i,1] = prime(primepi(f[i,1])+(row-1))); factorback(f)); A258851(n) = (n*sum(i=1, #n=factor(n)~, n[2, i]*primepi(n[1, i])/n[1, i])); \\ From A258851 A356155sq(row,col) = A258851(A246278sq(row,col)); A356155list(up_to) = { my(v = vector(up_to), i=0); for(a=1,oo, for(col=1,a, i++; if(i > up_to, return(v)); v[i] = A356155sq(col,(a-(col-1))))); (v); }; v356155 = A356155list(up_to); A356155(n) = v356155[n];
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