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A178057 Smallest prime number > a(n-1) that contains the n-th 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(n-1) that contains the n-th prime number as a substring. This is the 2nd row of an infinite array A[k,n] = Smallest k-almost prime number > a(n-1) that contains the n-th prime number as a substring. This is one plane of the infinite 3-D array A[j,k,n] = Smallest k-almost prime number > a(n-1) that contains the n-th 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(n-1) 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

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Last modified November 18 19:06 EST 2017. Contains 294894 sequences.