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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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 (nathaniel(AT)nathanieljohnston.com), Apr 30 2011
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LINKS
| Nathaniel Johnston, Table of n, a(n) for n = 1..90
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MAPLE
| 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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CROSSREFS
| Cf. A035497.
Sequence in context: A007627 A180525 A121877 * A058898 A123840 A063640
Adjacent sequences: A109899 A109900 A109901 * A109903 A109904 A109905
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KEYWORD
| nonn,base
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AUTHOR
| Paul Muljadi (paulmuljadi(AT)yahoo.com), Jun 22 2007
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EXTENSIONS
| Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 13 2007
a(24) - a(35) from Nathaniel Johnston (nathaniel(AT)nathanieljohnston.com), Apr 30 2011
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