A117737 Numbers such that the (positive) difference between the sum of the digits and the product of the digits is a prime number.

20, 24, 25, 27, 29, 30, 33, 34, 35, 37, 38, 42, 43, 45, 47, 49, 50, 52, 53, 54, 56, 57, 59, 65, 67, 70, 72, 73, 74, 75, 76, 78, 79, 83, 87, 92, 94, 95, 97, 101, 102, 104, 106, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 125, 126, 128, 131, 133, 140

Offset

1,1

Links

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

Example

97 is in the sequence because the sum of its digits is 16, the product of its digits is 63 and the difference between 16 and 63 is 47, which is a prime.

Maple

filter:= proc(n) local L;
L:= convert(n, base, 10);
isprime(abs(convert(L, `+`)-convert(L, `*`)))
end proc:
select(filter, [$1..1000]); # Robert Israel, Jan 22 2019

Mathematica

Select[Range[140], PrimeQ[Abs[Plus@@(x=IntegerDigits[#])-Times@@x]]&] (* Jayanta Basu, May 18 2013 *)

Prog

(PARI) sudig(i, suOrmul)= { local(nshft, resul) ; nshft = i ; resul = nshft % 10 ; nshft = nshft \ 10 ; while(nshft>0, if(suOrmul==0, resul += nshft % 10, resul *= nshft % 10 ) ; nshft \= 10 ; ) ; return(resul) ; } { for(n=10, 150, summ = sudig(n, 0) ; mull = sudig(n, 1) ; if( isprime(summ-mull), print1(n, ", ") ) ; ) ; } \\ R. J. Mathar, Apr 21 2006

Crossrefs

Cf. A000040.

Sequence in context: A199360 A199585 A093716 * A062908 A111323 A250289

Adjacent sequences: A117734 A117735 A117736 * A117738 A117739 A117740

Keyword

base,nonn

Author

Luc Stevens (lms022(AT)yahoo.com), Apr 14 2006

Extensions

More terms from R. J. Mathar, Apr 21 2006

Status

approved