A174926 - OEIS

%I #6 Jan 28 2012 14:46:22

%S 101,11,41,19,1601,251,1361,149,641,811,1009,12101,14401,1699,11969,

%T 2251,12569,1289,13241,1361,4001,4441,48409,10529,15761,62501,946769,

%U 4729,7841,8419,9001,9619,102409,10891,115601,12251,129641,11369,14449

%N Smallest prime which has a decimal representation which shows n^2 embedded in otherwise only decimal square digits 0, 1, 4 and 9.

%C There are four decimal square digits: 0 = 0^2 = 0, 1 = 1^2, 4 = 2^2, 9 = 3^2.

%C It is conjectured that sequence is infinite.

%C Some primes of the form n^2//1 = 10 * n^2 + 1 are in this sequence: for n = 1, 2, 5, ...

%C Note this curiosity of a double appearance of 1361 as  1//6^2//1 = p(6^2) = 1361 = p(19^2) = 1//19^2 or of 13691 = prime(1618) = 37^2//1 > 11369 = prime(1373) = 1//37^2 = p(37^2), 38th term of sequence

%e Let // denote concatenation of digits. Then:

%e 101 = prime(26) = 1//0^2//1.

%e 11 = prime(5) = 1^2//1.

%e 41 = prime(13) = 2^2//1.

%e 19 = prime(8) = 1//3^2.

%e 1601 = prime(252) = 4^2//0//1.

%e 251 = prime(54) = 5^2//1.

%e 1361 = prime(218) = 1//6^2//1.

%e 149 = prime(35) = 1//7^2.

%e 641 = prime(116) = 8^2//1.

%e 811 = prime(141) = 9^2//1.

%e 1009 = prime(169) = 10^2//9.

%e 12101 = prime(1448) = 11^2//0//1.

%Y Cf. A174884, A062584, A113616.

%K base,nonn

%O 1,1

%A Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 02 2010