A306926 - OEIS

A306926

A(n, k) is the k-th prime p > 10 where a string of exactly n zeros can be inserted somewhere into the decimal expansion such that the resulting number is also prime; square array, read by antidiagonals, downwards.

11, 13, 19, 17, 23, 17, 19, 31, 19, 13, 37, 41, 71, 23, 13, 41, 43, 73, 29, 23, 23, 53, 47, 79, 37, 73, 31, 17, 59, 53, 97, 59, 79, 43, 37, 17, 61, 59, 103, 71, 89, 107, 53, 19, 31, 67, 67, 149, 97, 179, 127, 59, 47, 43, 13, 71, 71, 151, 103, 223, 131, 61, 61

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..63.

EXAMPLE

Array starts as follows:

11, 13, 17, 19, 37, 41, 53, 59, 61, 67, 71, 79, 89, 97

19, 23, 31, 41, 43, 47, 53, 59, 67, 71, 89, 97, 107, 109

17, 19, 71, 73, 79, 97, 103, 149, 151, 157, 173, 181, 223, 229

13, 23, 29, 37, 59, 71, 97, 103, 127, 137, 139, 157, 181, 199

13, 23, 73, 79, 89, 179, 223, 233, 239, 241, 263, 269, 277, 281

23, 31, 43, 107, 127, 131, 137, 139, 149, 151, 163, 173, 179, 181

17, 37, 53, 59, 61, 67, 71, 107, 109, 151, 179, 193, 197, 211

17, 19, 47, 61, 67, 71, 157, 181, 197, 227, 313, 347, 353, 367

31, 43, 103, 113, 127, 137, 149, 157, 163, 173, 191, 241, 257, 277

13, 79, 113, 139, 163, 191, 293, 313, 349, 397, 433, 439, 443, 449

23, 79, 89, 137, 149, 151, 163, 181, 199, 229, 239, 241, 277, 311

41, 79, 131, 157, 167, 197, 199, 227, 229, 233, 241, 347, 349, 359

137, 167, 191, 197, 227, 277, 281, 313, 337, 353, 389, 421, 439, 449

Antidiagonals as a triangular array:

13, 19

17, 23, 17

19, 31, 19, 13

37, 41, 71, 23, 13

41, 43, 73, 29, 23, 23

53, 47, 79, 37, 73, 31, 17

59, 53, 97, 59, 79, 43, 37, 17

61, 59, 103, 71, 89, 107, 53, 19, 31

67, 67, 149, 97, 179, 127, 59, 47, 43, 13

71, 71, 151, 103, 223, 131, 61, 61, 103, 79, 23

PROG

(PARI) insert(n, len, pos) = my(d=digits(n), v=[], w=[]); for(y=1, pos, v=concat(v, d[y])); v=concat(v, vector(len)); for(z=pos+1, #d, v=concat(v, d[z])); subst(Pol(v), x, 10)

row(n, terms) = my(i=0); if(terms <= 0, print1(""), forprime(p=10, , for(k=1, #digits(p)-1, my(zins=insert(p, n, k)); if(ispseudoprime(zins), print1(p, ", "); i++; break)); if(i>=terms, print(""); break)))

array(rows, cols) = for(x=1, rows-1, row(x, cols))

array(12, 10) \\ Print initial 12 rows and 10 columns of array

CROSSREFS

Cf. A215417, A306920. Row 1 is A164329.

Sequence in context: A143365 A090137 A358573 * A205707 A136491 A357074

Adjacent sequences: A306923 A306924 A306925 * A306927 A306928 A306929

KEYWORD

nonn,tabl,base

AUTHOR

Felix Fröhlich, Mar 16 2019

STATUS

approved