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A174926
Smallest prime which has a decimal representation which shows n^2 embedded in otherwise only decimal square digits 0, 1, 4 and 9.
2
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
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
KEYWORD
base,nonn
AUTHOR
Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 02 2010
STATUS
approved