

A178057


Smallest prime number > a(n1) that contains the nth semiprime number as a substring.


1



41, 61, 79, 101, 149, 151, 211, 223, 251, 263, 331, 347, 353, 383, 397, 461, 491, 751, 1553, 1571, 1583, 1621, 1657, 1669, 1741, 1777, 1823, 2851, 2861, 2879, 2917, 2939, 3943, 4951, 10601, 11113, 11159, 11801, 11903, 12101, 12203, 12301, 12907, 13309
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Not to be confused with smallest semiprime number > a(n1) that contains the nth prime number as a substring. This is the 2nd row of an infinite array A[k,n] = Smallest kalmost prime number > a(n1) that contains the nth prime number as a substring. This is one plane of the infinite 3D array A[j,k,n] = Smallest kalmost prime number > a(n1) that contains the nth prime number as a substring in base j representation.


LINKS

Table of n, a(n) for n=1..44.


FORMULA

a(n) = MIN{p > a(n1) in A000040 such that A001358(n) as a string of decimal digits is a substring of p as a string of decimal digits}.


EXAMPLE

a(1) = 41 because 41 is the smallest prime whose decimal representation has "4" as a substring, and 4 = 2*2 is the 1st (smallest) semiprime (number of the form p*q where p and q are primes, not necessarily distinct).
a(2) = 61 because 61 is the smallest prime whose decimal representation has "6" as a substring, and 6 = 2*3 is the 2nd semiprime.
a(3) = 79 because 79 is the smallest prime > 61 whose decimal representation has "9" as a substring, and 9 = 3*3 is the 3rd semiprime.


CROSSREFS

Cf. A000040, A001358, A144565, A169798.
Sequence in context: A179826 A067832 A126242 * A169798 A110411 A145022
Adjacent sequences: A178054 A178055 A178056 * A178058 A178059 A178060


KEYWORD

nonn,base,less


AUTHOR

Jonathan Vos Post, May 18 2010


EXTENSIONS

Edited, corrected and extended by Ray Chandler, May 23 2010


STATUS

approved



