A176009 Smallest prime p = p(k) containing all decimal digits from "1" up to "k" (k = 1,2, ..., 9, 0).

11, 211, 1123, 1423, 112543, 1124653, 1234657, 112345687, 1123468597, 10123457689

Offset: 1

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Apr 06 2010

Keywords

• base
• fini
• full
• nonn

Comments

List of prime indices of these ten p(k):

5, 47, 188, 224, 10665, 87496, 95365, 6429837, 56789283, 460412186

Examples

			k = 1: 11 = prime(5), 1st term
k = 2: 21 is composite, 211 = prime(47), 2nd term
k = 3, digits 1,2 and 3: as 1+2+3 = 3 * 2 prime p(3) has d > 3 digits:
prime(216) = 1321 > 1231 = prime(202) > 1123 = prime(188), 3rd term
k = 4: 1423 = prime(224), k = 5: 112543 = prime(10665)
k = 6 = 2 * 3: 1124653 = prime(87496)
k = 7: p(7) = 1234657 = prime(95365) = prime(n)
Curious as sod(p(7)) = 1+2+3+4+6+5+7 = 28 = 9+5+3+6+5 = sod(95365) = sod(n),
7th term p(7) is a so-called Honaker prime
k = 8: 112345687 = prime(6429837)
k = 9 = 3 * 3: 1123468597 = prime(56789283)
All ten decimal digits: 10123457689 = prime(460412186)
		

Crossrefs

Cf. A037057, A037059, A175045.