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

1,1

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

Links

Table of n, a(n) for n=1..39.

Example

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.

Sequence in context: A083982 A369956 A029948 * A029949 A083152 A073053

Adjacent sequences: A174923 A174924 A174925 * A174927 A174928 A174929

Keyword

base,nonn

Author

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

Status

approved