A174926 Smallest prime which has a decimal representation which shows n^2 embedded in otherwise only decimal square digits 0, 1, 4 and 9.

101, 11, 41, 19, 1601, 251, 1361, 149, 641, 811, 1009, 12101, 14401, 1699, 11969, 2251, 12569, 1289, 13241, 1361, 4001, 4441, 48409, 10529, 15761, 62501, 946769, 4729, 7841, 8419, 9001, 9619, 102409, 10891, 115601, 12251, 129641, 11369, 14449

Offset: 1

Author

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

Keywords

• base
• nonn

Comments

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

It is conjectured that sequence is infinite.

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

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

Examples

			Let // denote concatenation of digits. Then:
101 = prime(26) = 1//0^2//1.
11 = prime(5) = 1^2//1.
41 = prime(13) = 2^2//1.
19 = prime(8) = 1//3^2.
1601 = prime(252) = 4^2//0//1.
251 = prime(54) = 5^2//1.
1361 = prime(218) = 1//6^2//1.
149 = prime(35) = 1//7^2.
641 = prime(116) = 8^2//1.
811 = prime(141) = 9^2//1.
1009 = prime(169) = 10^2//9.
12101 = prime(1448) = 11^2//0//1.
		

Crossrefs

Cf. A174884, A062584, A113616.