A357168 Starts of runs of at least 3 consecutive odd numbers whose prime factors are all prime-indexed primes.

1, 81, 121, 123, 153, 275, 1199, 1201, 1409, 1411, 2545, 3175, 4565, 5557, 5623, 6651, 7053, 8649, 11953, 15621, 16141, 16143, 20869, 22905, 28573, 36289, 39521, 51739, 52161, 56079, 56699, 56701, 63981, 76071, 77249, 79111, 105211, 125525, 144549, 153761, 167341

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000

Example

81 is a term since 81 = 3^4, 85 = 5 * 17, and 3 = prime(2), 5 = prime(3), 17 = prime(7) and 83 = prime(23) are all prime-indexed primes.

Mathematica

q[n_] := AllTrue[FactorInteger[n][[;; , 1]], PrimeQ[PrimePi[#]] &]; q[1] = True; v = q /@ {1, 3, 5}; seq = {}; Do[If[And @@ v, AppendTo[seq, k - 6]]; v = Join[Rest[v], {q[k]}], {k, 7, 10^5, 2}]; seq

Prog

(PARI) isokf(k) = my(f = factor(k)[, 1]); sum(i=1, #f, isprime(primepi(f[i]))) == #f; \\ A076610
isok(k) = (k % 2) && isokf(k) && isokf(k+2) && isokf(k+4); \\ Michel Marcus, Sep 16 2022

Crossrefs

Cf. A006450, A076610.

Subsequence of A357167.

A357169 is a subsequence.

Sequence in context: A129151 A039546 A223020 * A253261 A280587 A273372

Adjacent sequences: A357165 A357166 A357167 * A357169 A357170 A357171

Keyword

nonn

Author

Amiram Eldar, Sep 16 2022

Status

approved