A178057 Smallest prime number > a(n-1) that contains the n-th semiprime number as a substring.

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

Offset: 1

Author

Jonathan Vos Post, May 18 2010

Keywords

• nonn
• base
• less

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.

Examples

			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.

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}.

Extensions

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