[seqfan] Squares = concatenation of primes.
zak seidov
zakseidov at yahoo.com
Tue Dec 9 05:27:50 CET 2008
There are 15 squares that are concatenations of two 3-digit primes:
101761, 113569, 127449, 131769, 137641, 149769, 167281, 199809, 349281, 439569, 463761, 491401, 641601, 683929, 797449
What about other cases of s-digit squares that are concatenations of n primes with d digits (s=n*d)?
In our case s=6, n=2, d=3 there we have N(s,n,d) = 15.
Also:
N(2,2,1)=1 (one square 25 with prime digits)
N(3,3,1)=1 (one square 225 with prime digits )
N(4,4,1)=1 (one square 7225 with prime digits)
N(4,2,2)=3 (three squares 4761, 5329, 5929 with primes 47,61, 53,29, 59,29}
N(5,5,1)=2 (two squares 27225, 55225 with all digits prime}
N(6,6,1)=1 ( one square 235225 with prime digits)
N(6,3,2)=6 {six squares 136161, 178929, 231361, 534361, 591361, 677329
primes 13,61,61, 17,89,29, 23,13,61, 53,43,61, 59,13,61, 67,73,29}
Notice that we don't count square 670761 as 07 isn't 2-digit prime.
.........
N(9,3,3)=68 (68 squares all concatenations of three 3-digit primes:
103449241, 107557641, 109139809, 109181601, 109223401, 127757809, 139263601, 139877929, 151757761, 157577809, 179211769, 191241241, 191739409, 193293409, 193571569, 199967881, 211673401, 227617569, 227919409, 229613409, 251127409, 269977761, 283619281, 283821409, 307967401, 337199769, 337787641, 347337769, 349577809, 349727401, 373223761, 373919569, 383337241, 449397601, 467467641, 491641929, 503149761, 509359761, 509811241, 521163241, 523997881, 569251881, 571353409, 593263449, 607277449, 617373409, 619661449, 643281769, 653773761, 709103641, 733163929, 751911241, 761263281, 877877641, 881911809, 919241761, 967023409, 967769881, 971631241, 997233241, 997991281)
Anyone may wish to check/extend/submit these to OEIS?
thx, zak
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