A388993 Square array A(n,k) = A007913(A388981(n, k)), read by descending antidiagonals.

3, 2, 5, 5, 3, 7, 7, 7, 5, 11, 11, 11, 11, 7, 13, 3, 13, 13, 13, 11, 17, 2, 5, 17, 17, 17, 13, 19, 13, 3, 7, 19, 19, 19, 17, 23, 17, 17, 5, 11, 23, 23, 23, 19, 29, 2, 19, 19, 7, 13, 29, 29, 29, 23, 31, 19, 3, 23, 23, 11, 17, 31, 31, 31, 29, 37, 5, 23, 5, 29, 29, 13, 19, 37, 37, 37, 31, 41, 23, 7, 29, 7, 31, 31, 17, 23, 41, 41, 41, 37, 43

Offset

1,1

Comments

These are all primes, by the way A388981 is constructed. Each column contains successive primes starting from the one on the top.

Links

Antti Karttunen, Table of n, a(n) for n = 1..22155; the first 210 antidiagonals

Index entries for sequences computed from indices in prime factorization.

Example

The top left corner of the array:
k= |  1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18
---+-------------------------------------------------------------------------
1  |  3,  2,  5,  7, 11,  3,  2, 13, 17,  2, 19,  5, 23,  2,  3,  7, 29, 31,
2  |  5,  3,  7, 11, 13,  5,  3, 17, 19,  3, 23,  7, 29,  3,  5, 11, 31, 37,
3  |  7,  5, 11, 13, 17,  7,  5, 19, 23,  5, 29, 11, 31,  5,  7, 13, 37, 41,
4  | 11,  7, 13, 17, 19, 11,  7, 23, 29,  7, 31, 13, 37,  7, 11, 17, 41, 43,
5  | 13, 11, 17, 19, 23, 13, 11, 29, 31, 11, 37, 17, 41, 11, 13, 19, 43, 47,
6  | 17, 13, 19, 23, 29, 17, 13, 31, 37, 13, 41, 19, 43, 13, 17, 23, 47, 53,
7  | 19, 17, 23, 29, 31, 19, 17, 37, 41, 17, 43, 23, 47, 17, 19, 29, 53, 59,
8  | 23, 19, 29, 31, 37, 23, 19, 41, 43, 19, 47, 29, 53, 19, 23, 31, 59, 61,
9  | 29, 23, 31, 37, 41, 29, 23, 43, 47, 23, 53, 31, 59, 23, 29, 37, 61, 67,

Prog

(PARI)
up_to_cols = 210;
A388984list(up_to) = { my(v=vector(up_to), i=0); forstep(n=2, oo, 2, if(isprime(core(n)) && !isprimepower(n), i++; v[i] = n; if(i==up_to, return(v)))); };
v388984 = A388984list(up_to_cols);
A388984(n) = v388984[n];
up_to = binomial(up_to_cols+1, 2)
A388981sq(row, col) = if(1==row, A388984(col), my(f = factor(A388984(col))); for(i=1, #f~, f[i, 1] = prime(primepi(f[i, 1])+(row-1))); factorback(f));
A388993sq(row, col) = core(A388981sq(row, col));
A388993list(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] = A388993sq(col, (a-(col-1))))); (v); };
v388993 = A388993list(up_to);
A388993(n) = v388993[n];

Crossrefs

Cf. A003961, A007913, A388981, A388984.

Sequence in context: A167552 A094787 A132778 * A182289 A127738 A350900

Adjacent sequences: A388990 A388991 A388992 * A388994 A388995 A388996

Keyword

nonn,tabl

Author

Antti Karttunen, Sep 22 2025

Status

approved