A393798 - OEIS

A393798

a(n) is the least prime p such that a(n)-a(n-1) is a 3-smooth number, starting with a(1) = 2.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 131, 137, 139, 151, 157, 163, 167, 173, 179, 181, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 257, 263, 269, 271, 277, 281, 283, 307, 311, 313, 317, 349

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OFFSET

1,1

COMMENTS

Conjecture: This sequence is infinite.

LINKS

Table of n, a(n) for n=1..62.

EXAMPLE

a(1) = 2, the next prime is 3, 3-2=1 is a 3-smooth number, so a(2)=3.

a(30)=113, the next prime is 127, 127-113=14 which is not a 3-smooth number; the next prime after 127 is 131, 131-113=18 which is a 3-smooth number, so a(31)=131.

MATHEMATICA

p = 2; ans = {p}; Do[q = p; While[q = NextPrime[q]; diff = q - p; f = FactorInteger[diff]; s = Length[f]; f[[s, 1]] > 3]; p = q; AppendTo[ans, p], {i, 2, 72}]; Print[ans]

CROSSREFS

Cf. A000040, A003586.

Sequence in context: A095316 A095313 A095285 * A163849 A124591 A164837

Adjacent sequences: A393795 A393796 A393797 * A393799 A393800 A393801

KEYWORD

nonn,easy

AUTHOR

Lei Zhou, Feb 27 2026

STATUS

approved