A072274 -id:A072274 - cp's OEIS frontend

A247305 The smaller of two consecutive triangular numbers which are permutations of each other.

404550, 2653056, 3643650, 5633046, 6413571, 10122750, 10656036, 13762881, 19841850, 26634051, 32800950, 47848653, 56769840, 71634465, 89184690, 103672800, 137108520, 317053971, 345069585, 392714325, 408508236, 440762895, 508948560, 598735710, 718830486, 825215625

Offset: 1

K. D. Bajpai, Sep 11 2014

All the terms in sequence are congruent to 0 mod 9.

It appears that the digital root (repeated sum of digits) of the index +1 of a(n) in A000217 is 9 for each n>=1.o 0 mod 9. For example, 404550 = A000217(899), and 899+1 = 900 has digital root 9.

			a(1) = 404550 is in the sequence because {404550 and 405450} are a pair of consecutive triangular numbers having exactly the same digits.
a(2) = 2653056 is in the sequence because {2653056 and 2655360} are two consecutive triangular numbers having exactly the same digits.

K. D. Bajpai, Table of n, a(n) for n = 1..13000

Cf. A000217, A069567, A072274, A075093.

A247305 = {}; a = {1}; b = {2}; Do[t1 = n*(n + 1)/2; t2 = (n - 1)*(n - 1 + 1)/2; b = Sort[IntegerDigits[t1]]; If[a == b, AppendTo[A247305, t2]]; a = b, {n, 2, 7*10^4}]; A247305

lista(nn) = {for (n=1, nn, dt = vecsort(digits(t=n*(n+1)/2)); dnt = vecsort(digits((n+1)*(n+2)/2)); if (dt == dnt, print1(t, ", ")););} \\ Michel Marcus, Sep 13 2014

A163681 Smaller prime p in Ormiston pairs (p, q) with q - p = 72.

Original entry on oeis.org

1290719, 1477219, 1802419, 2520697, 2902519, 3327419, 3391697, 3498119, 4596419, 4641919, 4709519, 5521819, 5835619, 6091031, 6267419, 6642919, 6943919, 7118519, 7480519, 8241019, 8630519, 8934319, 8946919, 9859697

Offset: 1

Klaus Brockhaus, Aug 03 2009

An Ormiston pair (or rearrangement prime pair) is a pair of consecutive primes that use the same digits in a different order.

			(1802419, 1802491) is an Ormiston pair with gap 72, so 1802419 is in the sequence.

Jens Kruse Andersen, Ormiston Tuples
Eric Weisstein's World of Mathematics, Rearrangement Prime Pair

Subsequence of A069567.

Cf. A072274, A163863.

[ p: p in PrimesUpTo(10000000) | q-p eq 72 and a eq b where a is Sort(Intseq(p)) where b is Sort(Intseq(q)) where q is NextPrime(p) ];

Transpose[Select[Select[Partition[Prime[Range[800000]],2,1],Last[#]-First[#]==72&],Sort[IntegerDigits[First[#]]]==Sort[IntegerDigits[Last[#]]]&]][[1]]  (* Harvey P. Dale, Feb 14 2011 *)

Keyword base added by Klaus Brockhaus, Sep 18 2009

A217797 Smallest member of Ormiston prime 5-tuple.

Original entry on oeis.org

20847942560791, 21815124622913, 35581541330719, 40546521517819, 47950363950791, 54808830290791, 65923105730719, 84573572180719, 85950417240719

Offset: 1

Giovanni Resta, Oct 12 2012

Searched up to 10^14.

On 11 October 2012 Jens Kruse Andersen found a 6-tuple starting at 166389896360719, which is likely to be the smallest.

			a(1) is in the sequence since (20847942560791, 20847942560917, 20847942560971, 20847942561079, 20847942561097) are 5 consecutive primes whose decimal representations contain exactly the same digits.

Jens Kruse Andersen, Ormiston Tuples
E. W. Weisstein, MathWorld: Rearrangement Prime Pair

Cf. A072274 (Ormiston pairs), A075093 (Ormiston triples), A161160 (Ormiston quadruples).

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A247305 The smaller of two consecutive triangular numbers which are permutations of each other.

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A163681 Smaller prime p in Ormiston pairs (p, q) with q - p = 72.

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A217797 Smallest member of Ormiston prime 5-tuple.

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