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A217673
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Primes that produce primes twice in interbase translation to base 10 from both bases 2 and 3.
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3
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3660109, 69664477, 222606961, 234099253, 244425499, 252362347, 264492601, 289353943, 334710967, 365431051, 390680029, 400817629, 422451433, 530917927, 577666909, 594302287, 723691147, 738084037, 753950893, 788894581, 807284953, 827671849, 842959669, 985296679, 986511051, 1187799427, 1243788031, 1417131259, 1442128351, 1461773629, 1609808887, 1718949343, 1728686041, 1779144671, 1890591799, 2018095633, 2078547529, 2124366697, 2142242239, 2173576177, 2209776061, 2211799081, 2298824377, 2348568403
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OFFSET
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1,1
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COMMENTS
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This sequence first appeared publicly in April of 2010 at a debate-forum website as part of a claim of possible mediation of coincidental mathematical results. The 4th term here is the first to also translate once as a prime from base 4 to base 10, the 44th is the first to do so twice in succession, and, as can be seen, both lead with the digits 234 in base 10. An extension of the coincidence with the specifics of the 4th term is to be found -- beginning with this sequence's example -- in A217679 and A217680.
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LINKS
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EXAMPLE
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a(4) has base-2 representation 1101111101000001001000110101, and this string represents a base-10 prime. Its base-2 representation is 111000111011010001010110000110010010000001110010001001001100001111000101011000100000010101, also giving a base-10 prime. Similarly, in base 3 a(4) is represented by 121022111110210201, and this is prime when read as a base-10 number. That prime's base-3 representation is 210202210111201211102211000001022201, and this too reads as prime in base 10.
This particular example also remains prime through one interbase translation involving base 4, as noted in comments, and, separately, through two via base 5, with the numbers 31331001020311, 434412134003 and 24104134001242003 all base-10 primes.
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CROSSREFS
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KEYWORD
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nonn,base,less
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AUTHOR
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STATUS
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approved
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