cp's OEIS Frontend

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

%I A176009 #5 Sep 03 2018 20:40:39
%S A176009 11,211,1123,1423,112543,1124653,1234657,112345687,1123468597,
%T A176009 10123457689
%N A176009 Smallest prime p = p(k) containing all decimal digits from "1" up to "k" (k = 1,2, ..., 9, 0).
%C A176009 List of prime indices of these ten p(k):
%C A176009 5, 47, 188, 224, 10665, 87496, 95365, 6429837, 56789283, 460412186
%e A176009 k = 1: 11 = prime(5), 1st term
%e A176009 k = 2: 21 is composite, 211 = prime(47), 2nd term
%e A176009 k = 3, digits 1,2 and 3: as 1+2+3 = 3 * 2 prime p(3) has d > 3 digits:
%e A176009 prime(216) = 1321 > 1231 = prime(202) > 1123 = prime(188), 3rd term
%e A176009 k = 4: 1423 = prime(224), k = 5: 112543 = prime(10665)
%e A176009 k = 6 = 2 * 3: 1124653 = prime(87496)
%e A176009 k = 7: p(7) = 1234657 = prime(95365) = prime(n)
%e A176009 Curious as sod(p(7)) = 1+2+3+4+6+5+7 = 28 = 9+5+3+6+5 = sod(95365) = sod(n),
%e A176009 7th term p(7) is a so-called Honaker prime
%e A176009 k = 8: 112345687 = prime(6429837)
%e A176009 k = 9 = 3 * 3: 1123468597 = prime(56789283)
%e A176009 All ten decimal digits: 10123457689 = prime(460412186)
%Y A176009 Cf. A037057, A037059, A175045.
%K A176009 base,fini,full,nonn
%O A176009 1,1
%A A176009 Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Apr 06 2010