A342246 Numbers k such that k-1, k and k+1 are all composite with four, five and six (not necessarily distinct) prime factors respectively.

11151, 13455, 23375, 26271, 31311, 33776, 36125, 40375, 45495, 46375, 48411, 49049, 49167, 61335, 63125, 74151, 77895, 78111, 78351, 80271, 82575, 83511, 84591, 86031, 87375, 88749, 90207

Offset

1,1

Links

Dumitru Damian, Table of n, a(n) for n = 1..10456

Example

For k=11151 we have 11150 = 2 * 5^2 * 223 which is composite with four prime factors, 11151 = 3^3 * 7 * 59 which is composite with five prime factors and 11152 = 2^4 * 17 * 41 which is composite with six prime factors.

Mathematica

SequencePosition[PrimeOmega[Range[100000]], {4, 5, 6}][[;; , 1]]+1 (* Harvey P. Dale, Jul 30 2024 *)

Prog

(SageMath)
# The following SageMath algorithm will generate all terms up to 100000
L=[]
for n in [1..100000]:
    sum1, sum2, sum3 = 0, 0, 0
    for f in list(factor(n)):
        sum1+=f[1]
    for f in list(factor(n+1)):
        sum2+=f[1]
    for f in list(factor(n+2)):
        sum3+=f[1]
    if sum1==4 and sum2==5:
        if sum3==6:
            L.append(n+1)
print(L)
(PARI) for(n=3, 100000, if(bigomega(n-1)==4&&bigomega(n)==5&&bigomega(n+1)==6, print1(n, ", "))) \\ Hugo Pfoertner, Mar 07 2021

Crossrefs

Subsequence of A342258.

Cf. A001222, A014613, A014614, A046306.

Sequence in context: A205751 A205473 A250687 * A395761 A001727 A190793

Adjacent sequences: A342243 A342244 A342245 * A342247 A342248 A342249

Keyword

nonn

Author

Sean Lestrange, Mar 07 2021

Status

approved