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Search: id:A109902
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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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+0
1
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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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The subset of numbers of A035497 with the internal digits in the decimal representation all zero.
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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:
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CROSSREFS
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Cf. A035497.
Sequence in context: A113017 A007627 A121877 this_sequence A058898 A123840 A063640
Adjacent sequences: A109899 A109900 A109901 this_sequence A109903 A109904 A109905
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KEYWORD
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nonn
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AUTHOR
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Paul Muljadi (paulmuljadi(AT)yahoo.com), Jun 22 2007
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EXTENSIONS
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Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 13 2007
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