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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
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3, 5, 11, 17, 41, 107, 137, 347, 2111, 2657, 3527, 4421, 6761, 21011, 24371, 32057
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OFFSET
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1,1
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COMMENTS
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All terms are lesser of twin pairs.
The sequence is finite. In particular, there are no terms longer than 5 digits since 2*10^k for k=0,1,...,5 give all nonzero residues modulo 7, implying that adding 2 to some digit yields a multiple of 7. - Max Alekseyev, Apr 25 2010
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LINKS
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EXAMPLE
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2111 is in this sequence because all 2111, 4111, 2311, 2131 and 2113 are prime numbers.
32057 is in this sequence 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: # R. J. Mathar, Apr 16 2009
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MATHEMATICA
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spQ[p_]:=Max[IntegerDigits[p]]<8&&AllTrue[FromDigits/@Table[MapAt[ 2+#&, IntegerDigits[ p], n], {n, IntegerLength[p]}], PrimeQ]; Select[Prime[ Range[ 3500]], spQ] (* Harvey P. Dale, Nov 26 2022 *)
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PROG
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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
(PARI) has(n)=if(vecmax(Set(digits(n)))>7, return(0)); for(i=0, #digits(n)-1, if(!isprime(n+2*10^i), return(0))); 1
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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).
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KEYWORD
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nonn,full,fini,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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