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A178443 Two numbers k and l we call equivalent if they have the same vector of exponents with positive components in prime power factorization. Let a(1)=1, a(2)=3. If n>=3 is prime, then a(n) is the smallest prime greater than a(n-1); otherwise, a(n)>a(n-1) is the smallest number equivalent to n such that prime power factorization of a(n) contains only primes which already appeared in the sequence. 1
1, 3, 5, 9, 11, 15, 17, 27, 121, 187, 191, 275, 277, 573, 831, 14641, 14653, 109443, 109451, 131877, 161183, 249101, 249103, 254221, 214710409, 1603785503, 3146151623077, 23500268975459, 23500268975497, 352504034632455, 352504034632459, 675511501766876508493, 8283939628810696270871857123 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The sequence contains exactly 33 terms.

LINKS

Table of n, a(n) for n=1..33.

EXAMPLE

By the condition, a(12) should be more than a(11)=191. Since 12 has vector of positive exponents (2,1), then we seek already constructed prime terms p<q in the sequence and choose the smallest number of the form p^2*q>191. It is 275=5^2*11. Thus a(12)=275. Further, a(13) should be the nearest prime more than 275. It is 277.

PROG

(Sage)

@CachedFunction

def A178443(n):

    if n <= 2: return {1:1, 2:3}[n]

    if is_prime(n): return next_prime(A178443(n-1))

    psig_n = list(m for p, m in factor(n))

    primes_seen = sorted(set(filter(is_prime, map(A178443, range(2, n)))))

    possibles = (prod(p**m for p, m in zip(pvec, psig_n)) for pvec in Combinations(primes_seen, len(psig_n)))

    return min(p for p in possibles if p > A178443(n-1))

# [D. S. McNeil, Jan 01 2011]

CROSSREFS

Cf. A178442, A172980, A172999

Sequence in context: A064988 A166699 A191110 * A287421 A214214 A281505

Adjacent sequences:  A178440 A178441 A178442 * A178444 A178445 A178446

KEYWORD

nonn,fini,full

AUTHOR

Vladimir Shevelev, Dec 22 2010

STATUS

approved

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Last modified June 6 03:54 EDT 2020. Contains 334858 sequences. (Running on oeis4.)