A158641 Strong primes p: adding 2 to any one digit of p produces a prime number (no digits 8 & 9 in p)

3, 5, 11, 17, 41, 107, 137, 347, 2111, 2657, 3527, 4421, 6761, 21011, 24371, 32057

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