login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. 1
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:

  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, 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: A107932 A143365 A090137 * A205707 A136491 A268487

Adjacent sequences:  A306923 A306924 A306925 * A306927 A306928 A306929

KEYWORD

nonn,tabl,base

AUTHOR

Felix Fröhlich, Mar 16 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 19 20:41 EST 2020. Contains 331066 sequences. (Running on oeis4.)