A185300 -id:A185300 - cp's OEIS frontend

A214629 Primes p such that the sum of the digits plus the product of the digits is a prime.

11, 13, 19, 23, 29, 31, 37, 43, 53, 59, 61, 73, 79, 89, 97, 101, 223, 263, 283, 401, 409, 443, 601, 607, 809, 823, 829, 883, 1013, 1019, 1031, 1033, 1039, 1051, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1163, 1171, 1181, 1187, 1193, 1213, 1231, 1259

Offset: 1

Vicente Izquierdo Gomez, Aug 13 2012

			11 is in the sequence because A061762(11) = 3 is prime.

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

Cf. A061762, A344032. Primes in A185300.

f:= proc(n) local L;
   L:= convert(n,base,10);
   convert(L,`+`)+convert(L,`*`)
end proc:
select(p -> isprime(f(p)), [seq(ithprime(i),i=1..1000)]); # Robert Israel, May 07 2021

f[n_] := Module[{in = IntegerDigits[n]}, Times @@ in + Plus @@ in];Select[Prime[Range[300]], PrimeQ[f[#]] &]

{p in A000040: A061762(p) in A000040}. - R. J. Mathar, Aug 13 2012

A214746 Numbers n such that (sum of the square of the decimal digits of n) + (product of the square of decimal digits of n) is prime.

Original entry on oeis.org

1, 11, 13, 16, 19, 29, 31, 37, 59, 61, 73, 79, 91, 92, 95, 97, 101, 102, 104, 106, 110, 120, 140, 160, 201, 203, 205, 207, 210, 225, 230, 238, 250, 252, 270, 283, 302, 308, 320, 328, 380, 382, 401, 405, 409, 410, 449, 450, 490, 494, 502, 504, 506, 508, 520

Offset: 1

Michel Lagneau, Aug 01 2012

			283 is in the sequence because 2^2+8^2+3^2 + 2^2*8^2*3^2 = 77 + 2304 = 2381 is prime.

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

Cf. A185300.

dd:=func; [n: n in [1..520] | IsPrime(&+dd(n)+&*dd(n))]; // Bruno Berselli, Aug 02 2012

A:= proc(n) add(d^2, d=convert(n, base, 10)) ; end proc:
B:= proc(n) mul(d^2, d=convert(n, base, 10)) ; end proc:
isA:= proc(n) isprime(A(n)+B(n)) ; end proc:
for n from 1 to 1000 do if isA(n) then printf("%a, ", n) ; end if; end do:

is(n)=my(v=eval(Vec(Str(n))));isprime(sum(i=1,#v,v[i]^2)+prod(i=1,#v,v[i]^2)) \\ Charles R Greathouse IV, Aug 02 2012

A215059 Numbers n such that (sum of factorial of decimal digits of n) + (product of factorial of decimal digits of n) is prime.

Original entry on oeis.org

1, 10, 11, 12, 13, 15, 20, 21, 30, 31, 50, 51, 1000, 1001, 1002, 1010, 1011, 1012, 1020, 1021, 1100, 1101, 1102, 1110, 1111, 1112, 1120, 1121, 1200, 1201, 1210, 1211, 1339, 1344, 1345, 1354, 1356, 1359, 1365, 1366, 1368, 1386, 1393, 1395, 1434, 1435, 1443

Offset: 1

Michel Lagneau, Aug 01 2012

			1345 is in the sequence because (1! + 3! + 4! + 5! ) + (1! * 3! * 4! * 5!)  = 151 + 17280 = 17431 is prime.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A185300.

A:= proc(n) add(d!, d=convert(n, base, 10)) ; end proc:
B:= proc(n) mul(d!, d=convert(n, base, 10)) ; end proc:
isA:= proc(n) isprime(A(n)+B(n)) ; end proc:
for n from 1 to 1500 do if isA(n) then printf("%a, ", n) ; end if; end do:

fdpQ[n_]:=Module[{f=IntegerDigits[n]!},PrimeQ[Total[f]+Times@@f]]; Select[ Range[1500],fdpQ] (* Harvey P. Dale, Nov 26 2013 *)

A344021 Numbers k such that A061762(k) and k+A061762(k) are both prime.

Original entry on oeis.org

1, 12, 16, 32, 34, 54, 56, 78, 104, 106, 160, 232, 236, 250, 252, 298, 302, 304, 326, 328, 340, 362, 382, 388, 474, 490, 502, 508, 526, 560, 580, 610, 650, 656, 670, 676, 706, 740, 760, 838, 850, 890, 898, 928, 940, 980, 1004, 1006, 1024, 1028, 1042, 1048, 1082, 1084, 1152, 1190, 1192, 1246, 1248

Offset: 1

J. M. Bergot and Robert Israel, May 06 2021

			a(3) = 16 is a term because A061762(16) = 1*6+1+6=13 is prime and 16+13=29 is prime.

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

Cf. A061762, A185300.

f:= proc(n) local L;
L:= convert(n,base,10);
convert(L,`*`)+convert(L,`+`);
end proc:
filter:= proc(n) local t; t:= f(n); isprime(t) and isprime(n+t) end proc:
select(filter, [1,seq(i,i=2..10000,2)]);

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A214629 Primes p such that the sum of the digits plus the product of the digits is a prime.

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A214746 Numbers n such that (sum of the square of the decimal digits of n) + (product of the square of decimal digits of n) is prime.

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A215059 Numbers n such that (sum of factorial of decimal digits of n) + (product of factorial of decimal digits of n) is prime.

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Maple

Mathematica

A344021 Numbers k such that A061762(k) and k+A061762(k) are both prime.

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Maple