A092518 -id:A092518 - cp's OEIS frontend

A344466 Primes that occur as p + (digit product of p) for p in A092518.

29, 47, 67, 107, 109, 181, 251, 293, 331, 347, 431, 443, 457, 491, 547, 593, 631, 653, 659, 673, 743, 823, 827, 839, 929, 971, 977, 1091, 1129, 1181, 1231, 1237, 1279, 1321, 1327, 1423, 1433, 1447, 1471, 1483, 1493, 1499, 1553, 1559, 1579, 1601, 1777, 1823, 1867, 1871, 1951, 1993, 2113, 2137

Offset: 1

J. M. Bergot and Robert Israel, May 20 2021

Terms are unique and in numerical order.

There are terms that correspond to more than one member of A092518, such as 827 = 683+6*8*3 = 743+7*4*3.

			a(4) = 107 is a term because 83 = A092518(5) and 107 = 83+8*3.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A053666, A092518.

N:= 10000: # to get terms <= N
S:= {}:
p:= 1:
do
  p:= nextprime(p);
  if p >= N then break fi;
  L:= convert(p,base,10);
  if member(0,L) then next fi;
  q:= p + convert(L,`*`);
  if q <= N and isprime(q) then
     S:= S union {q};
  fi
od:
sort(convert(S,list));

A157677 Primes p such that p + (product of digits of p) is also prime.

Original entry on oeis.org

23, 29, 61, 67, 83, 101, 103, 107, 109, 163, 233, 239, 283, 293, 307, 347, 349, 401, 409, 431, 439, 443, 449, 499, 503, 509, 563, 569, 601, 607, 613, 617, 619, 653, 659, 677, 683, 701, 709, 743, 809, 907, 929, 941, 1009, 1013, 1019, 1021, 1031, 1033, 1039

Offset: 1

Kyle D. Balliet, Mar 04 2009

If p contains a zero, then p is trivially a member.

			83 is prime, and 83 + 8*3 = 89 which is also prime. 103 is prime, and 103 + 1*0*3 = 103 is also prime. Thus 89 and 103 are members.

Robert Israel, Table of n, a(n) for n = 1..10000

Union of A092518 and A056709.

Cf. A225303.

a := proc (n) local nn: nn := convert(ithprime(n), base, 10): if isprime(ithprime(n)+product(nn[j], j = 1 .. nops(nn))) = true then ithprime(n) else end if end proc: seq(a(n), n = 1 .. 180); # Emeric Deutsch, Mar 08 2009

Select[Prime[Range[175]], PrimeQ[# + Times @@ IntegerDigits[#]] &] (* Jayanta Basu, Apr 22 2013 *)

dprod(n)=n=digits(n); prod(i=1,#n,n[i])
is(n)=isprime(n) && isprime(n+dprod(n)) \\ Charles R Greathouse IV, Dec 27 2013

a(n) ~ n log n. - Charles R Greathouse IV, Apr 22 2013

More terms from Emeric Deutsch, Mar 08 2009

A157676 Numbers n such that n + (product of digits of n) is prime.

Original entry on oeis.org

1, 21, 23, 27, 29, 61, 67, 81, 83, 101, 103, 107, 109, 161, 163, 169, 233, 239, 253, 259, 283, 289, 293, 299, 307, 329, 341, 343, 347, 349, 361, 401, 409, 431, 437, 439, 441, 443, 449, 471, 473, 477, 493, 499, 503, 509, 529, 563, 569, 601, 607, 611, 613, 617

Offset: 1

Kyle D. Balliet, Mar 04 2009

			a(21) = 21 + (2)(1) = 23 (prime). a(67) = 67 + (6)(7) = 109 (prime). a(169) = 169 + (1)(6)(9) = 223 (prime).

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A157677, A092518.

fQ[n_] := PrimeQ[n + Times @@ IntegerDigits@n]; Select[ Range@1000, fQ@# &] (* Robert G. Wilson v, May 04 2009 *)

dprod(n)=n=digits(n);prod(i=1,#n,n[i])
is(n)=isprime(dprod(n)+n) \\ Charles R Greathouse IV, Dec 27 2013

a(n) ~ n log n. - Charles R Greathouse IV, Dec 27 2013

More terms from Robert G. Wilson v, May 04 2009

A092529 Primes p such that both the digit sum of p plus p and the digit product of p plus p are also primes.

Original entry on oeis.org

163, 233, 293, 431, 499, 563, 617, 743, 1423, 1483, 1489, 1867, 2273, 2543, 2633, 3449, 4211, 4217, 4273, 4547, 4729, 5861, 6121, 6529, 6637, 6653, 6761, 6857, 6949, 7681, 8273, 8431, 8837, 8839, 9649, 9689

Offset: 1

Ray G. Opao, Apr 08 2004

Intersection of A048519 and A092518.

Zeros are not permitted in p; thus, for example, 101 is not included. - Harvey P. Dale, May 25 2013

			a(2) = 233: 233+(2+3+3) = 233+8 = 241, which is prime. 233+(2*3*3) = 233+18 = 251, which is prime.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A048519, A092518.

filter:= proc(p) local L;
  if not isprime(p) then return false fi;
  L:= convert(p,base,10);
  if member(0,L) then return false fi;
  isprime(p + convert(L,`+`)) and isprime(p + convert(L,`*`))
end proc:
select(filter, [seq(i,i=3..10000,2)]); # Robert Israel, Feb 20 2024

pppQ[n_]:=Module[{idn=IntegerDigits[n]},!MemberQ[idn,0]&&And@@PrimeQ[ {n+ Total[idn], n+Times@@idn}]]; Select[Prime[Range[1200]],pppQ] (* Harvey P. Dale, May 25 2013 *)

More terms from Robert G. Wilson v, Apr 10 2004

cp's OEIS Frontend

A344466 Primes that occur as p + (digit product of p) for p in A092518.

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A157677 Primes p such that p + (product of digits of p) is also prime.

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A157676 Numbers n such that n + (product of digits of n) is prime.

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Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions

A092529 Primes p such that both the digit sum of p plus p and the digit product of p plus p are also primes.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Extensions