A115883 -id:A115883 - cp's OEIS frontend

A115882 Numbers k such that k + prime(k) gives a triangular number.

1, 20, 49, 65, 103, 176, 279, 284, 299, 437, 513, 553, 656, 973, 1271, 1779, 1921, 2156, 2312, 2347, 2554, 2759, 3176, 3379, 4008, 4028, 4132, 5255, 6354, 6764, 7116, 8299, 8334, 8366, 8723, 9277, 9755, 10092, 10475, 10631, 11429, 11842, 12633, 13157, 13627

Offset: 1

Giovanni Resta, Feb 06 2006

nonn

			103 + prime(103) = 103 + 563 = 666 = T(36).

T. D. Noe, Table of n, a(n) for n = 1..1000

Cf. A064371, A115883, A115886.

TriangularQ[n_] := IntegerQ[Sqrt[1 + 8*n]]; Select[Range[20000], TriangularQ[# + Prime[#]] &] (* T. D. Noe, Jan 27 2014 *)

isok(n) = ispolygonal(n + prime(n), 3); \\ Michel Marcus, Jan 25 2014

A115887 Triangular numbers equal to the difference between a prime number and its index.

Original entry on oeis.org

1, 3, 6, 10, 28, 105, 120, 153, 231, 465, 496, 1081, 1378, 1485, 1653, 1711, 2628, 3003, 3081, 3160, 4950, 5050, 5460, 6670, 6903, 8001, 8778, 10296, 11781, 14028, 15225, 16290, 19701, 20503, 21528, 21945, 22155, 24310, 24531, 25200, 27495

Offset: 1

Giovanni Resta, Feb 06 2006

nonn

			28=T(7)=p(13)-13.

Harvey P. Dale, Table of n, a(n) for n = 1..500

Cf. A115883.

Union[Select[Table[Prime[i]-i,{i,20000}],IntegerQ[Sqrt[8#+1]]&]] (* Harvey P. Dale, Jun 28 2012 *)

A236431 Numbers n such that both prime(n)+n and prime(n)-n give a triangular number.

Original entry on oeis.org

1, 513, 213796

Offset: 1

Michel Marcus, Jan 25 2014

Intersection of A115882 and A115883.
The corresponding primes are 2, 3673, 2955107.
No more terms up to 10^12. - Giovanni Resta, Jan 26 2014

			prime(1) is 2, and both 2+1=3 and 2-1=1 are triangular.

Cf. A115882, A115883.

Select[Range[214000],AllTrue[{Sqrt[8(Prime[#]-#)+1],Sqrt[8(Prime[#]+#)+ 1]},OddQ]&] (* Harvey P. Dale, Jul 22 2022 *)

lista(nn) = {p = primes(nn); for (n=1, #p, pn = p[n]; if (ispolygonal(pn - n, 3) && ispolygonal(pn + n, 3), print1(n, ", ")););}

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A115882 Numbers k such that k + prime(k) gives a triangular number.

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A115887 Triangular numbers equal to the difference between a prime number and its index.

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Author

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Mathematica

A236431 Numbers n such that both prime(n)+n and prime(n)-n give a triangular number.

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Mathematica

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