A062391 -id:A062391 - cp's OEIS frontend

A358438 a(1) = 4, a(2) = 6; then a(n + 1) is the smallest semiprime number > a(n) such that the sum of any three consecutive terms is a semiprime.

4, 6, 15, 25, 34, 35, 46, 62, 69, 74, 94, 106, 119, 121, 122, 134, 142, 146, 158, 169, 178, 206, 213, 214, 235, 249, 253, 265, 267, 299, 303, 319, 321, 334, 382, 395, 422, 445, 446, 454, 466, 469, 482, 514, 517, 538, 586, 589, 591, 623, 629

Offset: 1

Zak Seidov, Nov 17 2022

nonn

Do even numbers thin out as you look at larger and larger numbers of terms? - Charles R Greathouse IV, Nov 18 2022

			4 + 6 + 15 = 25 = 5*5, 6 + 15 + 25 = 46 = 2*23.

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

Cf. A062391 (analog for primes), A001358 (semiprimes).

R:= 4,6:
for i from 3 to 100 do
  s:= R[i-2]+R[i-1];
  for t from R[i-1]+1 do
    if numtheory:-bigomega(t) = 2 and numtheory:-bigomega(s+t)=2 then
      R:= R, t; break
    fi
od od:
R; # Robert Israel, Nov 18 2022

s = {4, 6}; p = 4; q = 6; r = q + 1; Do[While[2 != PrimeOmega[r] || 2 != PrimeOmega[p + q + r], r++]; AppendTo[s, r]; p = q; q = r; r++, {100}]; s

A153128 Prime numbers such that the sum of any 2 or 4 consecutive terms are averages of twin prime pairs and sum of any 3 or 5 consecutive terms are primes.

Original entry on oeis.org

11, 31, 41, 67, 131, 3121, 4229, 13159, 14081, 24631, 49877, 64921, 71789, 127051, 154871, 178621, 249677, 260011, 350729, 401473, 487397, 537883, 567767, 718423, 724499, 763621, 1004987, 1016611, 1043951, 1053529, 1090949, 1295113, 1309907

Offset: 1

Vladimir Joseph Stephan Orlovsky, Dec 19 2008

nonn

Cf. A153065, A062391, A153075

a=11;b=31;c=41;d=67;lst={a,b,c,d};Do[z=a+b+c+d+n;y=c+d+n;If[PrimeQ[z]&&n>d&&PrimeQ[n]&&PrimeQ[y]&&PrimeQ[a+b-1]&&PrimeQ[a+b+1]&&PrimeQ[b+c-1]&&PrimeQ[b+c+1]&&PrimeQ[c+d-1]&&PrimeQ[c+d+1]&&PrimeQ[d+n-1]&&PrimeQ[d+n+1]&&PrimeQ[a+b+c+d-1]&&PrimeQ[a+b+c+d+1]&&PrimeQ[b+c+d+n-1]&&PrimeQ[b+c+d+n+1],AppendTo[lst,n];a=b;b=c;c=d;d=n],{n,0,10!}];lst

A154502 Sum of any 3 consecutive numbers is prime and a(n+2)-(a(n+1)+a(n)) is prime, a(1)=3,a(2)=31.

Original entry on oeis.org

3, 31, 37, 71, 89, 157, 163

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jan 10 2009

nonn

3+31+37=71;37-(3+31)=3,...

Cf. A154484, A154485, A154486, A154487, A154488, A154493, A154494, A154495, A154496, A062391, A154497, A154498, A154500, A154501

a=3;b=31;lst={a,b};Do[c=Prime[n];p1=c+a+b;p2=c-(a+b);If[PrimeQ[p1]&&PrimeQ[p2],AppendTo[lst,c];a=b;b=c],{n,9,9!}];lst

NAME adapted to offset. - R. J. Mathar, Jun 19 2021

A168323 a(1)=3, a(2)=5; a(n+1) is the smallest prime number greater than a(n-1) and not equal to a(n) such that the sum of any three consecutive terms is a prime.

Original entry on oeis.org

3, 5, 11, 7, 13, 11, 17, 13, 23, 17, 31, 19, 47, 23, 61, 29, 67, 31, 83, 37, 103, 41, 107, 43, 113, 67, 127, 83, 137, 97, 139, 101, 149, 103, 157, 107, 167, 109, 173, 127, 179, 137, 193, 149, 199, 151, 227, 163, 229, 179, 233, 181, 239, 193, 241, 197, 263, 199, 271

Offset: 1

Vladimir Joseph Stephan Orlovsky, Nov 22 2009

nonn

Cf. A062391, A168322.

a=3;b=5;lst={a,b};Do[Do[If[PrimeQ[q]&&PrimeQ[a+b+q]&&q!=b,c=q;Break[]],{q,a+2,9!,2}];AppendTo[lst,c];a=b;b=c,{n,6!}];lst

cp's OEIS Frontend

A358438 a(1) = 4, a(2) = 6; then a(n + 1) is the smallest semiprime number > a(n) such that the sum of any three consecutive terms is a semiprime.

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A153128 Prime numbers such that the sum of any 2 or 4 consecutive terms are averages of twin prime pairs and sum of any 3 or 5 consecutive terms are primes.

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A154502 Sum of any 3 consecutive numbers is prime and a(n+2)-(a(n+1)+a(n)) is prime, a(1)=3,a(2)=31.

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A168323 a(1)=3, a(2)=5; a(n+1) is the smallest prime number greater than a(n-1) and not equal to a(n) such that the sum of any three consecutive terms is a prime.

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