A245381 Primes p such that sum and product of decimal digits of p are both semiprimes.

19, 37, 73, 127, 271, 1153, 1531, 1571, 3511, 5113, 5171, 5711, 7151, 11161, 11251, 12511, 15121, 16111, 25111, 111119, 111191, 111317, 111731, 113117, 113131, 113171, 115151, 131113, 131171, 131311, 131711, 171131, 311711, 511151, 515111, 711131, 911111, 1111213

Offset

1,1

Comments

The linked table includes probable primes. - Jens Kruse Andersen, Jul 21 2014

Links

K. D. Bajpai and Jens Kruse Andersen, Table of n, a(n) for n = 1..10000 (first 68 terms from K. D. Bajpai)

Example

127 is prime. 1 + 2 + 7 = 10 = 2 * 5 and 1 * 2 * 7 = 14 = 2 * 7, both are semiprime.
1571 is prime. 1 + 5 + 7 + 1 = 14 = 2 * 7 and  1 * 5 * 7 * 1 = 35 = 5 * 7, both are  semiprime.

Mathematica

Select[Prime[Range[100000]], PrimeOmega[(Times @@ IntegerDigits[#])] == 2 && PrimeOmega[(Plus @@ IntegerDigits[#])] == 2 &]

Prog

(PARI)
issemiprime(p) = p>0 && bigomega(p)==2
s=[]; forprime(p=2, 1200000, d=digits(p); if(issemiprime(sum(k=1, #d, d[k])) && issemiprime(prod(k=1, #d, d[k])), s=concat(s, p))); s \\ Colin Barker, Jul 20 2014
(PARI) f(n, b, s, d) = if(d, for(i=1, 9, if(b+bigomega(i)<=2, f(10*n+i, b+bigomega(i), s+i, d-1))), if(b==2 && bigomega(s)==2 && isprime(n), print1(n", ")))
for(d=1, 8, f(0, 0, 0, d)) \\ Faster program. f(0, 0, 0, d) prints d-digit terms. Jens Kruse Andersen, Jul 21 2014

Crossrefs

Cf. A000040, A001358, A007953, A007954.

Sequence in context: A061237 A158293 A107579 * A050528 A257074 A357935

Adjacent sequences: A245378 A245379 A245380 * A245382 A245383 A245384

Keyword

nonn,base

Author

K. D. Bajpai, Jul 20 2014

Status

approved