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A109902
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Happy primes of the form a*10^k + b with single-digit a and b, a > 0, k > 0.
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2
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13, 19, 23, 31, 79, 97, 103, 109, 409, 709, 907, 1009, 2003, 3001, 9001, 9007, 10009, 40009, 70009, 90001, 90007, 100003, 200003, 400009, 900001, 900007, 1000003, 2000003, 7000009, 20000003, 30000001, 400000009, 1000000009, 4000000009, 9000000001
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OFFSET
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1,1
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COMMENTS
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The subset of numbers of A035497 with the internal digits in the decimal representation all zero.
A number is in this sequence if and only if it is a prime of the form a00...00b, where (a,b) is one of (1,3), (1,9), (2,3), (3,1), (4,9), (7,9), (9,1), or (9,7). - Nathaniel Johnston, Apr 30 2011
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LINKS
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MAPLE
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A003132 := proc(n) local digs, i ; digs := convert(n, base, 10) ; add( (op(i, digs))^2, i=1..nops(digs)) ; end: isA035497 := proc(n) local nItr ; nItr := n ; if isprime(n) then while true do if nItr = 0 or nItr=4 or nItr = 16 or nItr = 20 or nItr = 37 or nItr = 42 or nItr =58 or nItr =89 or nItr = 145 then RETURN(false) ; elif nItr = 1 then RETURN(true) ; fi ; nItr := A003132(nItr) ; od ; else false ; fi ; end: isA109902 := proc(n) local digs, d ; if isprime(n) and n > 9 then digs := convert(n, base, 10) ; for d from 2 to nops(digs)-1 do if op(d, digs) <> 0 then RETURN(false) ; fi ; od ; RETURN(isA035497(n)) ; else RETURN(false) ; fi ; end: for i from 1 to 20000 do p := ithprime(i) : if isA109902(p) then printf("%d, ", p) ; fi ; od:
diglim:=20: dig:=[[1, 3], [1, 9], [2, 3], [3, 1], [4, 9], [7, 9], [9, 1], [9, 7]]: for k from 1 to diglim do for m from 1 to 8 do n:=dig[m][1]*10^k + dig[m][2]: if(isprime(n))then printf("%d, ", n): fi:od:od: # Nathaniel Johnston, Apr 30 2011
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MATHEMATICA
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Select[Sort[Flatten[With[{ab={{1, 3}, {1, 9}, {2, 3}, {3, 1}, {4, 9}, {7, 9}, {9, 1}, {9, 7}}}, Table[FromDigits[Join[PadRight[{ab[[n, 1]]}, i, 0], {ab[[n, 2]]}]], {n, 8}, {i, 9}]]]], PrimeQ] (* Harvey P. Dale, May 31 2013 *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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