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Search: id:A158641
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| A158641 |
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Strong primes p: adding 2 to any one digit of p produces a prime number (no digits 8 & 9 in p) |
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+0
1
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| 3, 5, 11, 17, 41, 107, 137, 347, 2111, 2657, 3527, 4421, 6761, 21011, 24371, 32057
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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All terms are lesser of twin pairs. Is the sequence finite with last term 32057?
The next term, if it exists, is greater than 18409199. [From Dmitry Kamenetsky (dkamen(AT)rsise.anu.edu.au), Apr 27 2009]
No more terms up to 4 billion.
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EXAMPLE
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2111 is OK because all 2111, 4111, 2311, 2131 and 2113 are prime numbers, 32057 is OK because all 32057, 52057, 34057, 32257, 32077 and 32059 are prime numbers.
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MAPLE
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Lton := proc(L) local i; add(op(i, L)*10^(i-1), i=1..nops(L)) ; end: isA158641 := proc(p) local pdgs, pplus, i ; if isprime(p) then pdgs := convert(p, base, 10) ; if convert(pdgs, set) intersect {8, 9} <> {} then false; else for i from 1 to nops(pdgs) do pplus := subsop(i=2+op(i, pdgs), pdgs) ; if not isprime(Lton(pplus)) then RETURN(false); fi; od: true; fi; else false; fi; end: for n from 1 do p := ithprime(n) ; if isA158641(p) then print(p) ; fi; od: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 16 2009]
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PROGRAM
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(PARI) test(p)={my(v=eval(Vec(Str(p)))); for(i=1, #v, if(v[i]>7, return(0))); for(i=0, #v-1, if(!isprime(p+2*10^i), return(0))); 1}; forprime(p=2, 4e9, if(isprime(p+2)&&test(p), print1(p", ")))
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CROSSREFS
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Cf. A050249, A158124, A158125 Weakly prime numbers (changing any one digit always produces a composite number).
Sequence in context: A129809 A040176 A092873 this_sequence A019386 A154622 A147251
Adjacent sequences: A158638 A158639 A158640 this_sequence A158642 A158643 A158644
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KEYWORD
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more,nonn
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AUTHOR
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Zak Seidov (zakseidov(AT)yahoo.com), Mar 23 2009
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EXTENSIONS
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Program and comment by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Sep 09 2009
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