A269260 For index k = A269230(n), the least prime with k consecutive digits 0, divided by 10^(k+1) and rounded down.

19, 10, 16, 16, 20, 30, 20, 15, 30, 26, 23, 27, 19, 17, 40, 30, 13, 13, 13, 24, 28, 22, 20, 10, 20, 30, 16, 10, 40, 13, 16, 11, 39, 10, 20, 20, 30, 10, 23, 16, 15, 30, 34, 56, 19, 28, 20, 20, 30, 20, 20, 90, 87, 68, 20, 25, 20, 16, 30, 40

Offset

1,1

Comments

For indices k not listed in A269230, the least prime with k digits '0', A037053(k), has these digits consecutively, in a single run. If k is listed in A269230, this is not the case (e.g., A037053(32) = 10...0603), and the most economical way to make a prime with k consecutive digits 0 is to put two (a priori nonzero) digits in front of the string of k '0's, i.e., p = a*10^(k+1) + b with a > 9.

This sequence lists these numbers a, and the corresponding prime (least prime with k consecutive digits 0) is simply nextprime(a*10^(k+1)).

If a is a multiple of 10, then b can have two nonzero digits, 11 <= b <= 99. Otherwise (b < 10), this prime is also the least prime with k+1 (consecutive) digits '0', A037053(k+1), and k+1 is listed in A085824 (unless a > 90). It is then obviously not the smallest prime with *exactly* k consecutive digits 0, but with *at least* k consecutive digits 0. This happens for (n,k,a,b) = (2,43,10,9), (24,108,10,7), (28,121,10,3), (34,132,10,7), (38,144,10,9), ...

Links

Table of n, a(n) for n=1..60.

Prog

(PARI) A269260(n, k=A269230(n))=for(a=1, 9e9, nextprime(a*10^(k+1))-a*10^(k+1)<10^(valuation(a, 10)+1)&&return(a)) \\ If the 2nd (optional) arg is given, the 1st arg 'n' is ignored. Otherwise the function A269230() must be defined.

Crossrefs

Sequence in context: A260328 A122549 A039942 * A050276 A107808 A214422

Adjacent sequences: A269257 A269258 A269259 * A269261 A269262 A269263

Keyword

nonn,base

Author

M. F. Hasler, Feb 22 2016

Status

approved