A378863 Prime numbers that yield a sphenic number when any digit is removed.

55511, 333337, 333383, 558533, 558587, 575651, 581557, 660557, 669937, 727777, 782861, 811037, 822389, 874477, 905551, 961663, 997699, 1116943, 1222271, 1302277, 1748189, 1766137, 1866677, 1999111, 2222333, 2289943, 2441111, 2444437, 2542229, 2575277, 2744699

Offset

1,1

Comments

The smallest prime with this property is 55511. Since being primes, the terms of this sequence end in 1, 3, 7 or 9. Unlike A371879, the penultimate digit can be 0. For example, 3388907 is a term whose penultimate digit is 0.

Links

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

Example

55511 is a term, because it is a prime number such that if the 5 is removed, the result is 5511 = 3 * 11 * 167, while if the 1 is removed, the result is 5551 = 7 * 13 * 61.

Mathematica

sphenicQ[n_] := FactorInteger[n][[;; , 2]] == {1, 1, 1}; q[n_] := AllTrue[FromDigits@ Drop[IntegerDigits[n], {#}] & /@ Range[IntegerLength[n]], sphenicQ]; Select[Prime[Range[200000]], q] (* Amiram Eldar, Dec 09 2024 *)

Prog

(PARI) has(n)=my(d=digits(n), t=2^#d-1); if(factor(fromdigits(vecextract(d, t-1)))[, 2]!=[1, 1, 1]~, return(0)); for(i=1, #d-1, if(d[i]==d[i+1], next); if(factor(fromdigits(vecextract(d, t-1<<i)))[, 2]!=[1, 1, 1]~, return(0))); 1
select(has, primes(10^6)) \\ Charles R Greathouse IV, Dec 09 2024

Crossrefs

Cf. A007304, A371879.

Sequence in context: A217692 A061740 A184094 * A345621 A346339 A345636

Adjacent sequences: A378860 A378861 A378862 * A378864 A378865 A378866

Keyword

nonn,base

Author

Gonzalo Martínez, Dec 09 2024

Status

approved