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 A111163 Triangular numbers that are sums of two consecutive primes. 8
 36, 78, 120, 210, 276, 300, 630, 946, 990, 1770, 1830, 2556, 2850, 3240, 3570, 4278, 4950, 5460, 8256, 9870, 10878, 11026, 12090, 12720, 20100, 20910, 23436, 26796, 31626, 34980, 41616, 43660, 46056, 55278, 56616, 57630, 59340, 66066, 73920 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Intersection of A000217 and A001043. - Michel Marcus, May 18 2015 LINKS Chai Wah Wu, Table of n, a(n) for n = 1..10000 (n = 1..472 from K. D. Bajpai, n = 473..1000 from T. D. Noe) EXAMPLE 36 = 8(8+1)/2 = 17 + 19. Therefore 36 belongs to the sequence. MAPLE P:=proc()local i, a, b, c; c:=1; for i from 1 to 1200000 do; a:=ithprime(i)+ithprime(i+1); b:=(-1+(sqrt(8*a+1)))/2; if  b=floor(b) then lprint(c, a); c:=c+1; fi; od; end:P(); # K. D. Bajpai, Jun 30 2013 MATHEMATICA Select[Table[Prime[n] + Prime[n + 1], {n, 4500}], IntegerQ[Sqrt[1 + 8# ]] &] (* Ray Chandler, Oct 22 2005 *) t = {}; n = 0; While[Length[t] < 100, n++; s = Prime[n] + Prime[n + 1]; If[TriangularQ[s], AppendTo[t, s]]]; t (* T. D. Noe, Jun 30 2013 *) PROG (PARI) {p=2; ct=0; while(ct<66, q=nextprime(p+1); s=p+q; if( issquare(8*s+1), print1(s, ", "); ct++); p=q)} \\ Klaus Brockhaus, Oct 22 2005 (Python) from sympy import nextprime as np from sympy import prevprime as pp n=1 t=n*(n+1)//2 while t>0: ....if t%2==0 and t>3: ........i=int(t//2) ........p=pp(i); q=np(p) ........if p+q==t : ............print(int(t)) ....n=n+1 ....t=n*(n+1)//2 # Abhiram R Devesh, May 17 2015 (Python) from __future__ import division from sympy import prevprime, nextprime, isprime A111163_list = [n*(n+1)//2 for n in range(3, 10**4) if not isprime(n*(n+1)//4) and prevprime(n*(n+1)//4)+nextprime(n*(n+1)//4) == n*(n+1)//2] # Chai Wah Wu, Feb 11 2018 CROSSREFS Cf. A000217 (triangular numbers), A001043 (sums of consecutive primes). Sequence in context: A255101 A255094 A261284 * A286430 A279901 A335276 Adjacent sequences:  A111160 A111161 A111162 * A111164 A111165 A111166 KEYWORD nonn AUTHOR Joseph L. Pe, Oct 20 2005 EXTENSIONS Extended by Ray Chandler and Klaus Brockhaus, Oct 22 2005 STATUS approved

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Last modified May 17 03:25 EDT 2022. Contains 353727 sequences. (Running on oeis4.)