A109902 Happy primes of the form a*10^k + b with single-digit a and b, a > 0, k > 0.
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
Offset: 1
Links
- Nathaniel Johnston, Table of n, a(n) for n = 1..90
Crossrefs
Cf. A035497.
Programs
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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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Mathematica
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 *)
Extensions
Edited by R. J. Mathar, Jul 13 2007
a(24) - a(35) from Nathaniel Johnston, Apr 30 2011
Comments