A141341 - OEIS

A141341

Totally Goldbach numbers: Positive integers n such that for all primes p < n-1 with p not dividing n, n-p is prime.

1, 2, 3, 4, 5, 6, 8, 10, 12, 18, 24, 30

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OFFSET

1,2

COMMENTS

As Browers et al. point out, A141340 = A141341 union {7,14,16,36,42,48,60,90,210}, A020490 = A141341\{5} and A048597 = A141341\{5,10}. The authors show that the first strategy of Deshouillers et al. to establish a bound (of 10^520) for A141340 is sufficient for then determining the totally Goldbach numbers and "leads us naturally to interesting questions concerning primes in a fixed residue class".

LINKS

Table of n, a(n) for n=1..12.

J-M. Deshouillers, A. Granville, W. Narkiewicz and C. Pomerance, An upper bound in Goldbach's problem, Math. Comp. 61 (1993), 209-213.

David van Golstein Brouwers, John Bamberg and Grant Cairns, Totally Goldbach numbers and related conjectures, The Australian Mathematical Society, Gazette, Volume 31 Number 4, September 2004.

Index entries for sequences related to Goldbach conjecture

CROSSREFS

Cf. A020490, A048597, A141340.

Sequence in context: A095381 A233205 A158292 * A238110 A211385 A373194

Adjacent sequences: A141338 A141339 A141340 * A141342 A141343 A141344

KEYWORD

fini,full,nonn

AUTHOR

Rick L. Shepherd, Jun 25 2008

STATUS

approved