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 A158641 Strong primes p: adding 2 to any one digit of p produces a prime number (no digits 8 & 9 in p) 0
 3, 5, 11, 17, 41, 107, 137, 347, 2111, 2657, 3527, 4421, 6761, 21011, 24371, 32057 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 LINKS Table of n, a(n) for n=1..16. EXAMPLE 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. MAPLE 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 MATHEMATICA 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 *) PROG (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", "))) \\ Charles R Greathouse IV, Sep 09 2009 (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 select(has, primes(3438)) \\ Charles R Greathouse IV, Mar 11 2016 CROSSREFS Cf. A050249, A158124, A158125 Weakly prime numbers (changing any one digit always produces a composite number). Sequence in context: A208572 A040176 A092873 * A019386 A283064 A154622 Adjacent sequences: A158638 A158639 A158640 * A158642 A158643 A158644 KEYWORD nonn,full,fini,base AUTHOR Zak Seidov, Mar 23 2009 EXTENSIONS Keywords full, fini from Max Alekseyev, Apr 25 2010 STATUS approved

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Last modified November 29 22:05 EST 2023. Contains 367452 sequences. (Running on oeis4.)