A389086 Primeshift array for primegap shift: Square array read by antidiagonals: A(1,col) = 3*col, and for row > 1, A(row,col) = A389084(A(row-1,col)).

3, 6, 7, 9, 35, 2, 12, 49, 26, 5, 15, 175, 4, 115, 13, 18, 91, 338, 25, 247, 23, 21, 245, 46, 2645, 169, 713, 19, 24, 14, 52, 95, 4693, 529, 209, 31, 27, 875, 10, 575, 403, 22103, 361, 1457, 11, 30, 343, 4394, 65, 3211, 253, 2299, 961, 1243, 47, 33, 455, 8, 60835, 299, 16399, 893, 68479, 121, 799, 113

Offset

1,1

Comments

This is a permutation of natural numbers > 1.

Links

Table of n, a(n) for n=1..66.

Index entries for primes, gaps between.

Index entries for sequences that are permutations of the natural numbers.

Example

The top left corner of the array:
k= |  1     2     3       4     5      6     7         8       9      10    11
---+---------------------------------------------------------------------------
1  |  3,    6,    9,     12,   15,    18,   21,       24,     27,     30,   33,
2  |  7,   35,   49,    175,   91,   245,   14,      875,    343,    455,  329,
3  |  2,   26,    4,    338,   46,    52,   10,     4394,      8,    598,  226,
4  |  5,  115,   25,   2645,   95,   575,   65,    60835,    125,   2185,   85,
5  | 13,  247,  169,   4693,  403,  3211,  299,    89167,   2197,   7657,  689,
6  | 23,  713,  529,  22103,  253, 16399,  437,   685193,  12167,   7843,  851,
7  | 19,  209,  361,   2299,  893,  3971,  589,    25289,   6859,   9823, 1159,
8  | 31, 1457,  961,  68479, 3503, 45167,  341,  3218513,  29791, 164641, 1333,
9  | 11, 1243,  121, 140459,  187, 13673,  517, 15871867,   1331,  21131,  979,
10 | 47,  799, 2209,  13583, 2491, 37553, 5311,   230911, 103823,  42347, 3431,

Prog

(PARI)
up_to = 105;
v130789 = readvec("b130789_to.txt"); \\ Prepared with gawk ' { print $2 } ' < b130789.txt > b130789_to.txt
A130789(n) = v130789[n];
invmap = Map(); for(i=1, #v130789, mapput(invmap, primepi(A130789(i)), i));
A389083(n) = mapget(invmap, n);
A389084(n) = { my(f=factor(n)); f[, 1] = apply(p->A130789(1+A389083(primepi(p))), f[, 1]); factorback(f); };
A389086sq(row, col) = { my(x=3*col); for(i=2, row, x = A389084(x)); (x); };
A389086list(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] = A389086sq(col, (a-(col-1))))); (v); };
v389086 = A389086list(up_to);
A389086(n) = v389086[n];

Crossrefs

Cf. A008585 (the topmost row), A130789 (the leftmost column).

Cf. A389083, A389084, A389085.

Cf. also A246278, A389088 for other primeshift arrays.

Sequence in context: A310134 A039591 A114082 * A343218 A185339 A189015

Adjacent sequences: A389083 A389084 A389085 * A389087 A389088 A389089

Keyword

nonn,tabl

Author

Antti Karttunen, Sep 24 2025

Status

approved