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Search: id:A089392
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| A089392 |
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Magnanimous primes: numbers n with following property. Let the digits of n be abcd. Then bcd+a, cd+ab, d+abc, abcd, etc. must all be primes. If n is a k-digit number then it must produce k such primes. |
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+0
8
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| 2, 3, 5, 7, 11, 23, 29, 41, 43, 47, 61, 67, 83, 89, 101, 227, 229, 281, 401, 443, 449, 467, 601, 607, 647, 661, 683, 809, 821, 863, 881, 2221, 2267, 2281, 2447, 4001, 4027, 4229, 4463, 4643, 6007, 6067, 6803, 8009, 8221, 8821, 20261, 24407, 26881, 28429, 40427
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Partition the digits of n by placing a '+' sign any where inside and the result of the expression is prime in every case. Conjecture: Sequence is infinite. 11 is the largest term with all odd digits. 2 is the only member with all even digits. In every other term only the least significant digit is odd rest are even by definition. Observation : All two digit primes with the most significant digit even are members.
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EXAMPLE
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2267 is a member which gives primes 2+267 = 269, 22+67 = 89, 226+7 = 233 and 2267 itself.
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MAPLE
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with(combinat): ds:=proc(s) local j: RETURN(add(s[j]*10^(j-1), j=1..nops(s))):end: for d from 1 to 6 do sch:=[seq([1, op(i), d+1], i=[[], seq([j], j=2..d)])]: for n from 10^(d-1) to 10^d-1 do sn:=convert(n, base, 10): fl:=0: for s in sch do m:=add(j, j=[seq(ds(sn[s[i]..s[i+1]-1]), i=1..nops(s)-1)]): if not isprime(m) then fl:=1: break fi od: if fl=0 then printf("%d, ", n) fi od od: (C. Ronaldo)
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CROSSREFS
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Cf. A089393, A089394.
Sequence in context: A078403 A129945 A046704 this_sequence A089695 A070027 A156658
Adjacent sequences: A089389 A089390 A089391 this_sequence A089393 A089394 A089395
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KEYWORD
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base,nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Nov 10 2003
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EXTENSIONS
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Corrected and extended by C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 25 2004
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