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Search: id:A090738
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| A090738 |
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Integers n such that the concatenation of n^2 and (n+1)^2 is prime. |
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1
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| 8, 12, 18, 20, 28, 40, 48, 82, 88, 92, 96, 98, 112, 128, 132, 140, 142, 218, 232, 238, 240, 246, 252, 272, 286, 288, 330, 332, 346, 356, 360, 376, 380, 450, 458, 460, 462, 466, 488, 500, 518, 532, 538, 550, 588, 590, 596, 602, 610, 612, 616, 630, 640, 646, 648
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OFFSET
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0,1
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COMMENT
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I conjecture this sequence to be infinite. Searching through the first 200000 values, I found 7000 primes, of which over 400 were "twins", i.e. both n^2*(n+1)^2 and (n+2)^2*(n+3)^2 were prime, where "*" denotes concatenation. I conjecture there to be an infinitude of such twins, and the obvious generalizations.
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EXAMPLE
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The first term, n=8 corresponds to the prime 6481, which is the concatenation of 8^2=64 and 9^2=81. The second term, n=12 corresponds to the prime 144169.
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MATHEMATICA
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For[i=1, i<200000, i=i+1, n=2i; e=IntegerPart[2 Log[10, n+1]]+1; x=10^e n^2 + (n+1)^2; y={n, x}; If[ PrimeQ[x], Save["primes.txt", y]]]
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CROSSREFS
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Adjacent sequences: A090735 A090736 A090737 this_sequence A090739 A090740 A090741
Sequence in context: A066428 A054397 A075818 this_sequence A085103 A087696 A015897
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KEYWORD
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nonn,base
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AUTHOR
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Alex Kontorovich (alexk(AT)math.columbia.edu), Jan 19 2004
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