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| A329416
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Among the pairwise sums of any ten consecutive terms there are exactly two prime sums: lexicographically earliest such sequence of distinct positive numbers.
(history;
published version)
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#22 by M. F. Hasler at Sun Feb 09 16:10:38 EST 2020
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#21 by M. F. Hasler at Sun Feb 09 16:09:48 EST 2020
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| NAME
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Lexicographically earliest sequence of distinct positive numbers such that amongAmong the pairwise sums of any ten consecutive terms there are exactly two prime sums: lexicographically earliest such sequence of distinct positive numbers.
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| CROSSREFS
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Cf. A329333 (3 consecutive terms, exactly 1 prime sum). See also A329450, A329452 onwards.).
Cf. A329405 (no prime among the pairwise sums of 3 consecutive terms).
Cf. A329406 .. A329410 (exactly 1 prime sum using 4, ..., 10 consecutive terms).
Cf. A329411 .. A329415 (exactly 2 prime sums using 3, ..., 7 consecutive terms).
See also "nonnegative" variants: A329450 (0 primes using 3 terms), A329452 (2 primes using 4 terms), A329453 (2 primes using 5 terms), A329454 (3 primes using 4 terms), A329449 (4 primes using 4 terms), A329455 (3 primes using 5 terms), A329456 (4 primes using 5 terms).
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| STATUS
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approved
editing
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Discussion
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| Sun Feb 09
| 16:10
| M. F. Hasler: Putting the relevant information to the front of NAME, since it was impossible to distinguish all the neighboring sequences from the "popup" titles truncated to 1 line.
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#20 by N. J. A. Sloane at Thu Nov 28 11:02:39 EST 2019
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#19 by Eric Angelini at Thu Nov 28 08:21:52 EST 2019
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#18 by Eric Angelini at Thu Nov 28 08:21:09 EST 2019
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| CROSSREFS
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Cf. A329333 (3 consecutive terms, exactly 1 prime sum). The 23 sequences in the range A329405 to A329427 develop the same idea with various numbers of consecutive terms and prime sums. See also A329450, A329452 onwards.
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| STATUS
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proposed
editing
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Discussion
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| Thu Nov 28
| 08:21
| Eric Angelini: Xrefs update.
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| 08:21
| Eric Angelini: > ianing Song: Hi Eric, you don't need A329423/4/6/7, right?
Right!
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#17 by Jianing Song at Thu Nov 28 07:58:11 EST 2019
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Discussion
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| Thu Nov 28
| 08:21
| Jianing Song: Hi Eric, you don't need A329423/4/6/7, right?
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#16 by Jianing Song at Thu Nov 28 07:57:46 EST 2019
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| CROSSREFS
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Cf. A329333 (3 consecutive terms, exactly 1 prime sum). The 2423 sequences in the range A329405 to A329428A329427 develop the same idea with various numbers of consecutive terms and prime sums. See also A329450, A329452 onwards.
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| STATUS
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approved
editing
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#15 by M. F. Hasler at Sun Nov 17 01:37:47 EST 2019
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#14 by M. F. Hasler at Sun Nov 17 01:37:38 EST 2019
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| COMMENTS
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Condition a(1) = 1 follows from minimality. Conjectured to be a permutation of the positive integers: a(10^6) = 10^6 + 2 and all numbers up to 10^6 - 7 have appeared at that point. - M. F. Hasler, Nov 15 2019
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| EXAMPLE
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a(1) = 1 is the smallest possible choice, there's no restriction on the byfirst minimalityterm.
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| STATUS
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approved
editing
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#13 by N. J. A. Sloane at Sat Nov 16 02:35:05 EST 2019
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| CROSSREFS
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Cf. A329333 (3 consecutive terms, exactly 1 prime sum). The 24 sequences in the range A329405 to A329428 develop the same idea with various numbers of consecutive terms and prime sums. See also A329450, A329452 onwards.
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Discussion
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| Sat Nov 16
| 02:35
| OEIS Server: https://oeis.org/edit/global/2836
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