A238715 -id:A238715 - cp's OEIS frontend

A238713 Least member of decadal prime triples: First prime beyond 10*A008470(n).

11, 41, 71, 101, 131, 191, 223, 311, 431, 461, 613, 641, 821, 853, 881, 1031, 1061, 1091, 1301, 1423, 1451, 1481, 1601, 1663, 1693, 1783, 1871, 1993, 2081, 2381, 2683, 2711, 3163, 3251, 3461, 3671, 3761, 3911, 4001, 4091, 4153, 4211, 4513, 4721, 4783, 4931

Offset: 1

M. F. Hasler, Mar 03 2014

nonn

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A008470, A008471, A238715.

for(d=1,999,primepi(10*(d+1))-primepi(10*d) >2|next; print1(nextprime(d*10+1)","))

is(n)=my(t=n%10); if(t==1, isprime(n) && if(isprime(n+2), isprime(n+6) || isprime(n+8), isprime(n+6) && isprime(n+8)), t==3 && isprime(n) && !isprime(n-2) && isprime(n+4) && isprime(n+6)) \\ Charles R Greathouse IV, Mar 04 2014

a(n) = nextprime(10*A008470(n)).

A238730 The largest prime in each decade (10k,10k+10) containing at least three primes.

Original entry on oeis.org

7, 19, 47, 79, 109, 139, 199, 229, 317, 439, 467, 619, 647, 829, 859, 887, 1039, 1069, 1097, 1307, 1429, 1459, 1489, 1609, 1669, 1699, 1789, 1879, 1999, 2089, 2389, 2689, 2719, 3169, 3259, 3469, 3677, 3769, 3919, 4007, 4099, 4159, 4219, 4519, 4729, 4789, 4937, 5237, 5419, 5449, 5479, 5507, 5659, 5749, 5869, 6709, 6829

Offset: 1

M. F. Hasler, Mar 03 2014

nonn

The initial term 7 does not correspond to a "decadal prime triple" according to the strict definition of A008470.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A008470, A008471, A238713, A238715.

f:= proc(k) local P;
   P:= select(isprime, [10*k+1,10*k+3,10*k+7,10*k+9]);
   if nops(P) >= 3 then max(P) fi
end proc:f(0):= 7:map(f, [$0..1000]); # Robert Israel, Jun 08 2020

p=0; for(d=1,999,2+p < (p=primepi(10*d)) && print1(precprime(d*10)","))

A238716 Run lengths of decadal prime triples.

Original entry on oeis.org

5, 2, 1, 2, 2, 3, 3, 1, 3, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 2, 1, 1

Offset: 1

M. F. Hasler, Mar 03 2014

Length of runs of "consecutive" (step = 3) values in A008470, which lists "prime triple decades", i.e., numbers m>1 such that the interval (10m,10m+10) contains at least 3 primes. The decades must be of the form m=3k+1, since for m=3k, 10m+3 and 10m+9 cannot be prime and for m=3k+2, 10k+1 and 10k+7 cannot be prime. Thus, "consecutive" prime triples are meant here in the sense of consecutive k-values.

			The first occurrence of 5 consecutive triples is: {11, 13, 17 (or 19)} ; {41, 43, 47} ; {71, 73, 79} ; {101, 103, 107 (or 109)} ; {131, 137, 139}. This corresponds to decades 1,4,7,10,13; i.e., the first 5 terms of sequence A008470. Therefore, a(1)=5.
The next "decadal prime triples" start at A238713(6)=191 and A238713(7)=223, they form the next run of length a(2)=2, since the decades A008470(6)=19 and A008470(7)=22 differ by the minimum which is 3, but the next one is further away.
The next term A238713(8)=311 starts an "isolated" decadal prime triple, i.e., the next "run" of length a(3)=1.
The next run of length 4 starts with decade m=541, and the next occurrence of 5 consecutive triples starts with decade m=910052463685 (found by J. K. Andersen).

Cf. A008470, A008471, A238713, A238715.

{d=10; p=primepi(d); i=0; while( po=p, p=primepi( d+=10 ); p>2+po && i++ && (p=primepi(d+=20)) && next; i || next; print1(i",");i>=3 && print1("/*",[nextprime(d-10-30*i),precprime(d-30)]"*/ ");i=0;)}

cp's OEIS Frontend

A238713 Least member of decadal prime triples: First prime beyond 10*A008470(n).

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A238730 The largest prime in each decade (10k,10k+10) containing at least three primes.

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A238716 Run lengths of decadal prime triples.

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PARI