A393237 - OEIS

A393237

Numbers k such that k is a 7-smooth number, and k + 11, k + 13, k + 17, k + 19 are prime number quadruples.

90, 180, 810, 1470, 3240, 18900, 21000, 67200, 268800, 6561000, 21609000, 36750000, 243855360, 252000000, 321489000, 463050000, 756315000, 1913625000, 136559001600, 290424960000, 5664669696000, 182967724800000, 257698037760000, 1054333217387520, 1138465843200000

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..25.

EXAMPLE

67200 is in this sequence because 67200 = 2^7 * 3 * 5^2 * 7 which is a 7-smooth number, and 67200 + 11 = 67211, 67200 + 13 = 67213, 67200 + 17 = 67217, and 67200 + 19 = 67219 compose as a prime number quadruple.

PROG

(PARI)

listA002473(lim)=my(v=List(), t); for(a=0, logint(lim\1, 7), for(b=0, logint(lim\7^a, 5), for(c=0, logint(lim\7^a\5^b, 3), t=3^c*5^b*7^a; while(t<=lim, listput(v, t); t<<=1)))); Set(v)

lista(lim) = select(k->isprime(k+11) && isprime(k+13) && isprime(k+17) && isprime(k+19), listA002473(lim))

CROSSREFS

Cf. A002473, A007530.

Sequence in context: A255792 A255785 A366740 * A119896 A179697 A211442

Adjacent sequences: A393234 A393235 A393236 * A393238 A393239 A393240

KEYWORD

nonn

AUTHOR

Zhicheng Wei, Feb 06 2026

STATUS

approved