A277118 -id:A277118 - cp's OEIS frontend

A277119 Numbers n such that A277118(n) = 17.

470, 746, 995, 3061, 3425, 3486, 11359, 12233, 16181, 17142, 18717, 24976, 30991, 48138, 61882, 62293, 63833, 99770, 103132, 110651, 111769, 112407, 117282, 138939, 149251, 150296, 161457, 173581, 174029, 176096, 188691, 221737, 225322, 233565, 235084, 237651, 262176, 266889, 279382, 281398, 284617, 290328, 292830

Offset: 1

Vladimir Shevelev and Peter J. C. Moses, Sep 30 2016

nonn

A277118 takes only the values 0, 3, 5, 7, 9, 11, 13, 15, and 17, so these are the indices of maximal terms in A277118.
Let p=A001359(n-1). Then n is in the sequence if and only if we have seven consecutive primes: either {p=30t+29 (t>=0),p+2,p+8,p+12,p+18,p+24,p+30} or {p,p+2,p+8,p+14,p+20,p+24,p+30} or {p,p+2,p+8,p+14,p+18,p+24,p+30}, but p+32 is composite. In the case, when also p+32 is prime, the numbers
{n} form sequence A277512.

			a(1)=470, then we have seven primes: p=A001359(469) =30089, 30091, 30097, 30103,30109,30113,30119, but 30121 is composite (cf. comment).

Vladimir Shevelev, Peter J. C. Moses, Constellations of primes generated by twin primes, arXiv:1610.03385 [math.NT], 2016.

Cf. A001359, A277118, A277512.

A277512 Numbers n such that A277118(n) = 15.

Original entry on oeis.org

13, 88, 5708, 15095, 18300, 20718, 23424, 45625, 59638, 63958, 66438, 71747, 78239, 154992, 225235, 411285, 418434, 550190, 571439, 743873, 883958, 938420, 989479, 1169298, 1198004, 1256049

Offset: 1

Vladimir Shevelev and Peter J. C. Moses, Oct 18 2016

Let p=A001359(n-1). Then n is in the sequence if and only if we have one of constellations of eight consecutive primes: {p=30t+29 (t>=0), p+2,p+8, p+12,p+18, p+24,p+30,p+32}, {p,p+2,p+8,p+14,p+20,p+24,p+30,p+32}, {p,p+2, p+8,p+14, p+18,p+24,p+30,p+32}.

			a(1)=13, then we have one of three mentioned in comment constellations of 8 consecutive primes: p=A001359(12)=149, 151, 157, 163, 167, 173, 179 and 181.

Vladimir Shevelev, Peter J. C. Moses, Constellations of primes generated by twin primes, arXiv:1610.03385 [math.NT], 2016.

Cf. A001359, A277118, A277119.

A277255 Let A_n defined in the same way as A159559, but with initial term prime(n); a(n) is the smallest number m such that A_(n+1)(m) - A_n(m) > 6 or a(n)=0 if there is no such m.

Original entry on oeis.org

0, 13, 0, 0, 9, 0, 0, 13, 0, 15, 0, 9, 0, 0, 11, 0, 17, 13, 11, 7, 5, 3, 2, 0, 11, 7, 5, 3, 2, 7, 5, 3, 2, 15, 0, 9, 0, 7, 5, 3, 2, 7, 5, 3, 2, 2, 9, 0, 7, 5, 3, 2, 0, 0, 11, 0, 7, 5, 3, 2, 2, 7, 5, 3, 2, 3, 2, 7, 5, 3, 2, 11, 7, 5, 3, 2, 3, 2, 2, 3, 2, 11, 7

Offset: 2

Vladimir Shevelev and Peter J. C. Moses, Oct 22 2016

nonn

A277118 is a subsequence. In contrast to A277118, the sequence contains some terms greater than 17. The first occurrence for 19 is n = 7061; the first occurrence for 21 is n = 214612 and the first occurrence for 23 is n = 30572.

Peter J. C. Moses, Table of n, a(n) for n = 2..5001
Vladimir Shevelev, Peter J. C. Moses, Constellations of primes generated by twin primes, arXiv:1610.03385 [math.NT], 2016.

Cf. A159559, A277118.

a(n)=2 if and only if prime(n+1) - prime(n) >=8.

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A277119 Numbers n such that A277118(n) = 17.

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A277512 Numbers n such that A277118(n) = 15.

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A277255 Let A_n defined in the same way as A159559, but with initial term prime(n); a(n) is the smallest number m such that A_(n+1)(m) - A_n(m) > 6 or a(n)=0 if there is no such m.

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